A Professional Journal Published by the International Federation of Technical Analysts

24

Inside This Issue
2 The Impact of Freely Accessible Large Language Models on
Market Sentiment Monitoring
10 Multiple Regression Analysis
38 Minute-Generated Price Values for Time Series Analysis
44 Validation of a Trading System: Monte Carlo Analysis Applied
to the IS & OOS Architec-ture
48 The Impact of Machine Learning and Computer Vision to
Predict an Opening Range Breakout on E-Mini S&P 500
62 The 5% Canary“Even if I knew that
tomorrow the world would go
to pieces, I would still plant myapple tree”—Martin Luther
ISSN 2409-0271

Letter From the Editor
By Dr. Rolf Wetzer, CFTe, MFTA

Dear IFTA Colleagues and Friends,
This year, for the first time, the Journal is being delivered after the conference. The 2023
conference was held in Jakarta. It took place for the 36th time and was hosted by AATI, theassociation of our Indonesian colleagues. As always—since 1988, the presentations were
informative and of high quality, and the time was characterised by hospitality and meeting
new and old friends.
And yet, the year was much different than usual. The world seems to be recovering slowly
from COVID. All national associations reported that direct meetings around the world are
only slowly starting up again. We will regain our former strength, but the disease has left its
mark on people's behaviour. In addition, the world is slipping intoa phase of armed conflict the likes of which we have not seen for a long time. We will also
overcome this together, but a veil of uncertainty is slowly settling over societies. The
easy and carefree days seem further away at the moment.
It is therefore important that we do our part to promote friendship, cooperation, andtogetherness in our sector. IFTA provides the platform for this, and many nations andcountries contribute to it. This Journal is another example. The articles, and the work on
the journal itself, come from people all over the world. Technical analysis unites!
As every year, I would like to thank everyone who has contributed to its creation.
First and foremost, of course, to NAAIM and to Susan Truesdale. For years we have been
allowed to publish articles from their programme. This year, it is the contribution ofAndrew Thrasher, the winner of the NAAIM Founders Award.
We would also like to thank all the authors, the Linda Bernetich team, who year after
year bring the Journal into a form that never ceases to amaze me. Many thanks forthat. And finally, I would like to thank Regina Meani, who has been providing valuable
contributions and book reviews for over a decade now.
I wish the entire IFTA family a blessed and happy 2024. May it be peaceful and bringmany new friendships.

It is therefore
important that we do
our part to promote
friendship, cooperation,and togetherness in our
sector.

Best regards,
Dr. Rolf Wetzer, CFTe, MFTA

IFTA JOURNALEDITORIAL
Dr. Rolf Wetzer, CFTe, MFTA
Editor and Chair of the Editorial Committee
Rolf.Wetzer@ifta.org
Mohamed El Saiid, MFTA, CFTe
melsaiid@hc-si.com
Regina Meani, CFTe
regina.meani@gmail.com

Send your queries about advertisinginformation and rates to admin@ifta.org

2024 EDITION

Letter From the Editor
By Dr. Rolf Wetzer, CFTe, MFTA ..........................................................................................Inside front cover
ArticlesThe Impact of Freely Accessible Large Language Models on Market Sentiment Monitoring
By Andrea Bolognesi........................................................................................................................................2
Multiple Regression Analysis
By Davide Pandini, Ph.D., MFTA, CFTe, CMT, CSTA ...................................................................................10
Minute-Generated Price Values for Time Series Analysis
By Christoph T. Wildensee, Ph.D., MFTA......................................................................................................38
Validation of a Trading System: Monte Carlo Analysis Applied to the IS & OOS Architecture
By Michael Trequattrini, CSTA.................................................................................................................... 44
MFTA Paper
The Impact of Machine Learning and Computer Vision to Predict an Opening Range Breakout on
E-Mini S&P 500
By Edzard Wiener, Ph.D, MFTA, CFTe.......................................................................................................... 48
NAAIM Paper
The 5% Canary
By Andrew Thrasher, CMT.............................................................................................................................62
Book Review
Encyclopedia of Chart Patterns by Thomas N. Bulkowski
Reviewed by Regina Meani, CFTe.................................................................................................................72

Author Profiles.................................................................................................................................................. 73
IFTA Staff.............................................................................................................................................................75
IFTA Board of Directors....................................................................................................................................75

The IFTA Journal is published annually by the International Federation of Technical Analysts, 1300 Piccard Dr., Suite LL 14 Rockville, MD 20850 USA.
© 2024 International Federation of Technical Analysts. All rights reserved. No part of this publication may be reproduced or transmitted in any
form or by any means, electronic or mechanical, including photocopying for public or private use, or by any information storage or retrieval system,without prior permission of the publisher.

IFTA.ORG PAGE 1

IFTA JOURNAL

2024 EDITION

The Impact of Freely Accessible Large
Language Models on Market Sentiment
Monitoring
Abstract
This article explores how freely accessible large language
models capable of performing natural language processing
on publicly available financial documents can be applied
to technical analysis. I argue that, because these artificial
intelligence models only have access to publicly available
financial information such as news reports, news articles,
investment forums, public discussions, and earnings
transcripts, they can constitute a proxy to gauge retailinvestors sentiment’s strength and direction (i.e., either
positive or negative), thus providing valuable information toa technical analyst. This paper proposes possible applications
in trend analysis (to anticipate trend continuations, reversals,or breakouts) as well as other areas of technical analysis suchas testing support and resistance areas and trading bands.
Lastly, this paper suggests the use of retail investors' sentiment
analysis can be extended to other aspects of interest to atechnical analysis such as event studies or uncovering retail
information asymmetry.

Introduction
This paper takes as a starting point the release on theeighth of March 2023 of Google Bard, the first large language
model (LLM) chatbot developed by Google AI. This comes at apoint in time where the exponential growth in the availability
and size of unstructured textual data sets (articles, reports,
forum discussions) coincided with the absence of tools freely
available to all technical analysts (regardless of their coding
background) to analyze these large amounts of unstructured
textual data. Additionally, in recent years, the unbiased analysisof large amounts of this type of data has gained recognition
to understand market sentiment around certain securities or
events, thus constituting a potential competitive advantage.
To uncover the possible applications of Google Bard intechnical analysis, this article starts by introducing natural
language processing (NLP) and its applications to thefinancial markets as well as how the release of LLMs capableof performing NLP on publicly available news reports, news
articles, investment forums, public discussions, earnings
transcripts can be used as a proxy to gage retail investors
attention and sentiment around certain security and/or event.
I argue for the inclusion of LLMs such as Google Bard in atechnical analyst’s toolkit by highlighting how it can be used as
an additional data point when investigating price trends, chartpatterns, and signals validity.

PAGE 2 IFTA.ORG

Andrea Bolognesi
University College of London
andrea.bolognesi11@gmail.com

Understanding NLP Within Large
Language Models
What Is Natural Language Processing
Natural language processing is a subfield of artificial
intelligence and computational linguistics that focuses on theinteraction between computers and human language. It involves
the development and application of algorithms and models
to enable computers to understand and manipulate natural
language. In this particular case, I will focus on two of the tasks
it can perform: Information extraction and sentiment analysis.
Information extraction (IE) is the process of automaticallyextracting structured information from unstructured orsemi-structured text data (such as news articles). By applying
information extraction techniques to a news article, website,or report, we can extract key entities, events, facts & data,
thereby gaining structured and meaningful information fromthe unstructured text. Similarly, sentiment analysis aims toanalyze sentence structure, word choice and other elements
to understand the tone of the article and identify positive or
negative sentiments expressed towards specific entities or
topics.
The interesting aspect of the results of information extraction
and sentiment analysis is that it can inform us on possible
developments in stock returns and trading volumes before they
happen. For instance, sentiment studies on articles published
on a specific company often have contemporaneous or shortterm effects on stock prices and trading volumes (Kearney andLiu, 2014). Similarly, particular types of information publishedin public news is associated to abnormal returns following its
release (Chan, 2003).
NLP Integration in Large Language Models
In the past, NLP algorithms were often inaccessible tomost investors as they necessitated coding experience andtechnical expertise to implement and maintain effectively. Even
commercially available options were inaccessible as subject tolicensing restrictions imposed by large companies or research
institutions. As a result, investors were largely excluded fromaccessing NLP models and integrating sentiment analysis into
their toolkit.
However, a significant shift occurred with the release of public
LLMs. The introduction of GPT-3 in November 2022 marked
a significant turning point, providing broader access to NLP
capabilities. More importantly, the launch of public LLMs withreal-time data access, exemplified by Google Bard in March
2023, democratized NLP on press releases and publicly available
documents to all investors. This accessibility to NLP, coupled

IFTA JOURNAL

with real-time data, opened new avenues for investors to gain
insights and make informed decisions based on sophisticatedlanguage analysis.
Literature Review
Given the recent emergence of freely accessible LLMs, very
limited research has been published on the specific impact ofrendering NLP available to all investors and the overall impact
of being able to freely run NLP algorithms on the entiretyof publicly available financial data & news. Nonetheless,considering the significant attention cast on NLP in the past
decade, researchers have taken interest in the new data provided
by complex NLP analysis to relatively small batches of data over alimited time span.
Researchers have shown a strong interest in exploring thecorrelation between sentiment expressed in annual reports andfuture earnings/stock performance. Li (2006) conducted a study
utilizing a linear regression sentiment-based trading strategy
on annual company reports spanning nine years. The study
concluded that an increase in risk sentiment in annual reports is
associated with significantly lower future earnings.
While most of the previous research has focused on sentiment
analysis of news articles, Tetlock (2007) found that high levelsof media pessimism exert temporary downward pressure on
market prices and induce high market trading volume. Tetlock etal. (2008) further refined the analysis and concluded that stock
market prices respond to negative words with a small, one-day
delay. This finding was supported by Carretta et al. (2011) andEngelberg et al. (2012), who designed a news sentiment-based
trading strategy centered around short selling and negative
news. Their study showed an impressive 180% return over a
two-and-a-half-year sample period (2005–2007). Ferguson et al.
(2012) reaffirmed and extended this research by demonstratingthat the predictive relationship between media content andfirms' returns is particularly significant for low-visibility firms
with low market capitalization and high book-to-market ratio.
In contrast, other researchers have focused on sentiment
analysis of information available only to professional investors,
such as analysts' reports. These studies have indicated that
sentiment analysis on analysts' reports seems to be less effectivein establishing a relationship with stock market returns. Kothari
et al. (2009) found that disclosures from analysts appear to beheavily discounted by the market.
Furthermore, researchers have applied NLP techniques toother financial documents, such as earnings press releases(Henry, 2008) or earnings conference calls and Q&A sessions(Doran et al., 2010). These studies have shown that both negativeand positive sentiments in these documents have significant
explanatory power for accompanying abnormal returns.

2024 EDITION

Relevance to Financial Markets
The current research seems to point out a strong predictive
relationship between negative sentiment in news articles,
earnings press releases & earnings calls, and abnormal firms'
returns. Taking this into account, this paper will now investigate
how the NLP data produced by freely accessible LLMs can help us
as technical analysts.
This paper suggests these freely available LLMs measure theattention, intention, and consensus amongst retail investors,
the roots of this interpretation are suggested by Ren (2023)
which highlights Internet search as the “most important channel
through which retail investors gather and process information”.
Freely available LLMs, such as Google Bard, differ from nonpublicly available NLP models due to the fact they can only accessand perform sentiment analysis and information extraction on
publicly available information (i.e., News reports, news articles,
investment forums, public discussions, earnings transcripts…
but not analysts’ reports). This means their results suffer fromthe same information disadvantages as retail investors are
subject to compared to institutional investors who have accessto more researched information via analyst reports (Cheng et al.,2016; Jung et al., 2018; Soltes, 2014). These new accessible LLMs,
therefore, reflect the sentiment of the content and discussions
available to retail investors and thus, following the literature
mentioned, allow us to anticipate an increase in interest fromthese retail investors on the concerned stocks. Given this, Barberand Odean (2011) provides a helpful insight into the behavioral
characteristics of these retail investors. They note the tendencyof retail investors to be influenced by various behavioral biases(such as being influenced by past experience and exposure
to media) that often lead them to contribute to a short-term
overreaction in stock prices paving the way to an eventual
reversal.
This paper will thus contend accessible LLMs can be potentiallyrelevant to technical analysis by using Google Bard sentiment
analysis data on publicly available news, articles, and retailinvestors' discussions as a proxy for retail investors' interest andthus a tool to identify the short-term overreaction characterizing
retail investors. In this case, we refer to the situation where theGoogle Bard retail sentiment shows an opposite trend to theprice movement (i.e., retail sentiment is falling while the price ismoving in an uptrend and/or the retail sentiment is rising while
the price is moving in a downtrend) as a price trend driven by
non-retail investors (i.e., professional or institutional investors)
who are likely to be more informed, less subject to the aforementioned behavioral biases and hence lead to a more enduring
price trend less subject to reversals.

IFTA.ORG PAGE 3

IFTA JOURNAL

2024 EDITION

Table 1

Applications to Technical Analysis
For the sake of simplicity, this paper will base its analysis
on the results of a single LLM, Google Bard. The usefulness of
Google Bard will vary depending on the specific prompt used.
In this study, prompts of the type "what is the sentiment fromretail investors around y stock since [insert timeframe] monthby month" or "by performing sentiment analysis on news
reports, news articles, investment forums, public discussions,earnings transcripts available to retail investors, createa table for retail investors sentiment around y stock since[insert timeframe] by month" will be used to retrieve tangible
numerical data from 0 to 100 to display the intensity anddirection of retail investors sentiment; for the purpose of thisstudy any value below 40 is considered as "negative sentiment"from retail investors.
Analysis of Trends
In technical analysis, the notion of a trend holds significant
importance in understanding and interpreting price movements.
A trend, in essence, refers to the prevailing direction of pricemovement over a certain period. Technical analysts employ arange of tools and methodologies to discern two fundamental
aspects related to price trends: the direction in which the price iscurrently moving and the probability of its continuation.
The main way Google Bard can be applied to technical analysis
is by helping us determine the probability of trend continuation;
for this use, Google Bard can help us track the strength anddirection of retail investors' attention by analyzing news,
forum conversations and all other material published by andavailable to retail investors. This can then be compared to thedirection and strength of the current trend to better understandwhich types of investors are driving the current trend andthus evaluate its sustainability. This paper will use the average
directional indicator (ADX), outlined in Wilder (1978) to help

PAGE 4 IFTA.ORG

determine the strength of a trend regardless of its direction(upward or downward). The ADX provides a value ranging from 0
to 100, with higher values (>40) indicating a stronger trend.
The analysis of ADX value in conjunction with the retailinvestors’ attentions’ strength values yields two possible
scenarios with separate interpretations: On the one hand, if ADX
rises or remains constant while Google Bard indicates retailinvestor’s attention is on the rise then it can be concluded that it
is very likely the current price trend is driven by retail investors
and thus subject to a reversal as the current price trend is likely
to be driven by short-term sentiment rather than long-term
fundamentals. Inversely, if the ADX remains constant or rises
while retail investor’s attention declines it can be concluded
that it is very likely the current trend is driven by institutional
investors and is thus less subject to reversal and instead much
more likely to be sustainable.
Given the ADX is a directionless indicator, one of the possible
limitations of this analysis is the incorrect identification of thedrivers behind the price trend. In other words, in the current
state of the analysis, an increase in retail investors' interest
doesn’t necessarily mean they are pushing the price in the same
direction as the trend. To reduce the likelihood of incorrect driver
identification, the trend analysis can be refined with an analysisof the direction of the security’s price trend in conjunction
with Google Bard’s retail investors’ sentiment analysis. If thedirection of the retail investor’s attention coincides with thecurrent price trend (i.e., upwards price trend accompanied
by an increase in retail investor’s attention characterized bypositive sentiment) then it can be concluded with even more
precision that the trend is indeed driven by retail investors andthus subject to a reversal as the current price trend is likely
to be driven by short-term sentiment rather than long-term
fundamentals.

IFTA JOURNAL

2024 EDITION

This can be seen in the period highlighted in red in Figure 1, the strong upwards price trend from Nov-21 to Jan-22 is likely to be driven
by retail investors as Google Bard sentiment analysis highlights a rise in positive sentiment around PFE. Given that this trend is likely tobe driven by retail investors, a subsequent reversal is likely to happen as seen from Jan-22 to Mar-22.
Table 2

Figure 1

IFTA.ORG PAGE 5

IFTA JOURNAL

2024 EDITION

Determining Entry Points
The identification of an optimal entry point is very important
for a technical analyst, as it facilitates the initiation of a trade ata favorable price level, thereby maximizing potential gains andmitigating associated risks.
This paper suggests that an analysis of the relative strength
index (RSI) in conjunction with Google Bard retail investors'
sentiment can offer insight into whether the price of overboughtor oversold security is fueled by retail investors or institutional
investors to help ascertain whether the current price presents
the characteristics of a good entry-point for either short or longpositions. The RSI is a momentum oscillator that measures the
speed and change of price movements. It provides a numericalvalue between 0 and 100, suggesting whether the stock isoverbought (When RSI>70) and thus indicating that buyingpressure has driven the price to an unsustainable level orconversely, that the stock is oversold (when RSI<30) potentiallypresenting a buying opportunity.
Once again, two possible scenarios can be observed, if the RSI
indicator rises above 70 signaling a security is overbought and
Google Bard indicates a rise in positive sentiment amongst retailinvestors, then it can be concluded that it is very likely that thebuying pressure that has driven the price to an unsustainable
Figure 2

PAGE 6 IFTA.ORG

level is coming mainly from retail investors thus signaling thatthe current stock price may be a good entry point for a shortposition given the likelihood of a subsequent normalizationin price levels. Inversely, when the RSI indicator rises above
70 signaling a certain security is overbought and Google Bard
indicates a decrease in positive sentiment amongst retailinvestors, it is likely that in this case, the buying pressure
originates amongst institutional investors possessing better
market knowledge suggesting the reason behind the pricemovement should be further investigated as the reversal may not
be immediate.
An instance of this can be seen in Figure 2 at the orange
marker line. As the RSI reaches above 70, while retail investors'
sentiment declines, this leads to uncertain price fluctuations
through the following month (Dec-21).
The inverse reasoning can be applied when the RSI indicator
drops below 30.
Support and Resistance Areas
Support and resistance areas refer to specific price levels or
range on a chart where buying or selling pressure is expected
to be significant. Support levels are considered the price levels
where demand is expected to be strong enough to prevent

IFTA JOURNAL

further price declines, while resistance levels are price levels
where selling pressure is anticipated to be strong enough toimpede further price increases. The utilization of moving average
charts offers a method for identifying support and resistancelevels. Specifically, when the price approaches a moving average
from below and subsequently rebounds, it implies the presenceof potential support at that level. Conversely, when the priceapproaches a moving average from above and encounters
resistance, it signifies a potential resistance area.
That said, different resistance support areas have different
strengths, some support or resistance levels may be more robust
and respected, while others may be more easily breached.
The strength of a support or resistance level is determinedby multiple factors such as the number of times it has beentested, the volume of trading at that level, the psychology of themarket… This paper aims to use Google Bard retail investors'
sentiment analysis to identify the types of buyers and sellers
behind a certain support or resistance level to attempt todetermine its strength. Following the same assumptions as in
the previous parts, if it could be concluded resistance (support)
levels backed by retail investors might be considered less strongas they might have less researched underlying reason why theprice of the security is not likely to rise above (drop below) thatlevel or simply be fueled by news overreaction.
When analyzing moving averages in conjunction with Google
Bard retail sentiment, If the price approaches a moving average
from above (below) in a way suggesting the existence of a
support/resistance area while Google Bard indicates positive
retail (negative) investors sentiment, this may indicate thesupport (resistance) area is backed by institutional investors.
As such it is likely to be tested and easily pierced as it isunlikely to be backed by strong fundamental analysis. if Google
Bard indicates opposite retail investors' sentiment to the2024 EDITION

aforementioned, the observed support/resistance area is likely
to be stronger and thus lead to a price reversal.
Analysis of Trading Bands
Google Bard can be utilized in conjunction with trading
bands to enhance the reliability of their signals. Trading bands
encompass bands that are plotted above and below the priceline, aiming to offer a relative delineation of high and low prices.
Common examples of trading bands include the Bollinger andDonchian bands. The application of trading bands facilitates
the identification of transient price overreactions, typicallydiscerned when the price surpasses the upper band or falls below
the lower band. In tandem with trading bands, Google Bard canprovide valuable insights regarding the underlying participants
driving the observed price dynamics, thus contributing to theevaluation of the signal's validity.
If the price moves above the upper band (below the lowerband) in conjunction with an increase in positive (negative)
sentiment from retail investors, this confirms the signal islikely highlighting a short-term overreaction. Consequently, an
impending reversal of the prevailing trend would be anticipated.
This is shown in Figure 3 as the price moves below the lower
Bollinger band accompanied by a sudden drop in retail investors
sentiment; this price movement is very likely to have been ashort-term overreaction fueled by retail investors because, as
expected, price bounces back up immediately after.
However, if the signal arises with retail investors either
exhibiting indeterminate sentiment or expressing sentimentcounter to the price movement's direction, this suggests that the
bands may have identified the initiation of a new trend rather
than a transient overreaction. Consequently, further analysisof the fundamental drivers underpinning the recent pricefluctuations is advised.

Figure 3

IFTA.ORG PAGE 7

IFTA JOURNAL

2024 EDITION

Extensions
Retail Information Asymmetry
Understanding the extent of information asymmetry is vitalas it aids investors in assessing whether they possess uniqueinsights conferring them with a competitive edge or if it aligns
with the general knowledge already priced into the market. For
technical analysts, understanding market developments canhelp in price analysis and trend recognition. This paper suggests
Google Bard as a tool to check for information asymmetry andverify whether retail investors and/or the street has picked up on
specific news or market developments. Given an event, new data
point, or piece of information x, a prompt of the type “has x been
cited in articles, reports, retail investors forums?” or “provide
the number of news articles, reports, retail investors forums…
citing x in the past” allows technical analysts to check for theseinformation asymmetries before entering a trade in order toavoid sudden shifts in price, volume, or trading activity as x gets
priced in by retail investors.
Additionally, through the same types of prompts, Google
Bard allows technical analysts to check for the reactivity ofthe market by comparing the time from retail investors pickup certain pieces of information and the following increase in
trading volume driven by these retail investors.
Event Studies and Market Sentiment
Google Bard can also be used as a source of information as partof an event study. By prompting it to perform sentiment analysis
on all documents related to a certain event y, it is possible togather important information in certain types of event studies aswell as plot the evolution of sentiment following the event y. This
paper suggests prompts of the type “by performing sentiment
analysis on all articles, reports, retail investors forums releasedin the past [select timeframe], what has been the sentimentaround an event y and how has it evolved?” where y can bea certain company’s product launch, marketing campaign,
management communication, legal issues, defective products…
This can then be cross-checked with specialized industry reports
to confront retail investor’s reactions to certain event is in linewith more knowledgeable and researched positions held byinstitutional investors.
For instance, if we were to enquire about retail investors
sentiment around a company’s product launch and it returned
an extremely positive sentiment from retail investors, this could
then be compared to specialized industry reports which may
display different sentiments by offering a more complete picture.
It is then in the best interest of the technical analyst to keep
this information in mind when entering specific positions that
may be affected by the possible shift in sentiment from retailinvestors towards the institutional consensus as they bridge theinformational gap.
Rising (and Falling) Wedges
A rising wedge is a technical pattern that frequently appears inbear markets and serves as an indicator of a potential reversal.
This pattern is characterized by the upward movement ofprices, where pivot highs and lows gradually converge towards
a singular point referred to as the apex on charts. Correctly
PAGE 8 IFTA.ORG

identifying the rising wedge pattern is extremely important
for technical analysts as it serves as an indicator of a potential
downside movement as the price is expected to break out of
the narrowing range and undergo a bearish reversal. Inversely,
a falling wedge on the other hand suggests a potential upside.
The rising wedge pattern (falling wedge pattern) is usuallyaccompanied by signals that improve the accuracy of its
recognition such as a decrease (increase) in trading volume as
the pattern progresses. In this case, volume decrease shows
sellers are consolidating their energy before they start pushing
the price action lower towards the breakout.
This paper suggests Google Bard can be used to verify whether
retail investors or institutional investors are behind the decreasein trading volume signaling the potential breakout of the pattern.
In other words, knowing the investors behind the decreasein trading volume may play an important role in the correct
identification of the pattern, if it is retail investors driving thedecrease in trading volume this might lead to a failed pattern due
to a lack of genuine market conviction or a temporary disruption
in the anticipated price movement. This paper thus suggests
a prompt of the type “by analyzing retail investor sentiment,
retail-specific news, retail investors forum posts, market
participation analysis and trading activity data, are retailinvestors behind the notable decrease in trading volume in thepast [insert timeframe]?” in order to ascertain the type of groups
of investors behind the accompanied trading volume changes.

Conclusion
In this paper, we have explored various ways to integrate
Google Bard in a technical analyst tool kit to complement andimprove trend analysis, price analysis and other chart patternrecognition. Nevertheless, this paper recommends technicalanalysts to exercise a high degree of caution when using Google
Bard as a proxy for retail investors sentiment as attention due tothe lack of transparency behind Bard’s NLP algorithms. Technicalanalysts are thus encouraged to use Google Bard’s applications
listed throughout this paper as an additional data point in thecontext of a more in-depth analysis.

References
Barber, B. M., & Odean, T. (2011). The behavior of individual investors.
Handbook of the Economics of Finance, 2, 1533-1570.
Carretta, A., Farina, V., Graziano, E. A., & Reale, M. (2011). Does investor
attention influence stock market activity? The case of spin-off deals.
SSRN. Retrieved from http://ssrn.com/abstract=1930861
Cheng, Q., Du, F., Wang, X., & Wang, Y. (2016). Seeing is believing:
Analysts' corporate site visits. Review of Accounting Studies, 21(4),1245-1286. doi:10.1007/s11142-016-9368-9
Colm Kearney, & Sha Liu. (2014). Textual sentiment in finance: A surveyof methods and models. International Review of Financial Analysis,
33, 171-185. doi:10.1016/j.irfa.2014.02.006
Doran, J. S., Peterson, D. R., & Price, S. M. (2010). Earnings conference
call content and stock price: The case of REITs. Journal of Real Estate
Finance and Economics, 45(2), 402-434.
Durnev, A., & Mangen, C. (2011). The real effects of disclosure tone:
Evidence from restatements. SSRN. Retrieved from http://ssrn.com/
abstract=1650003

IFTA JOURNAL

2024 EDITION

Engelberg, J., Reed, A. V., & Ringgenberg, M. C. (2012). How are shorts
informed? Short sellers, news, and information processing. Journalof Financial Economics, 105(2), 260-278.
Henry, E. (2008). Are investors influenced by how earnings press
releases are written? The Journal of Business Communication, 45(4),363-407.
Jung, M. J., Wong, M. H. F., & Zhang, X. F. (2018). Buy-side analysts andearnings conference calls. Journal of Accounting Research, 56(3),913-952. doi:10.1111/1475-679X.12180
Kothari, S. P., Li, X., & Short, J. E. (2009). The effect of disclosures bymanagement, analysts, and business press on cost of capital, return
volatility, and analyst forecasts: A study using content analysis. The
Accounting Review, 84(5), 1639-1670.
Li, F. (2006). Do stock market investors understand the risk sentimentof corporate annual reports? SSRN. Retrieved from http://ssrn.com/
abstract=898181
N.J. Ferguson, J. Guo, H.Y.T. Lam, & D. Philip. Media content and stock
returns: The predictive power of press.
N.J. Ferguson J. Guo H.Y.T. Lam D. Philip Media content and stock returns:
The predictive power of press
Ren, W., & Zhou, J. (2019). Stock price reaction to CEO messages on social
media: Evidence from Twitter. Journal of Accounting and Economics,
68(2-3), 101253. doi:10.1016/j.jacceco.2019.06.001
Soltes, E. (2014). Private interaction between firm management andsell-side analysts. Journal of Accounting Research, 52(1), 245-272.
doi:10.1111/1475679X.12037
Tetlock, P. C. (2007). Giving content to investor sentiment: The role ofmedia in the stock market. Journal of Finance, 62, 1139-1168.
Tetlock, P. C., Saar-Tsechansky, M., & Macskassy, S. (2008). More thanwords: Quantifying language to measure firms' fundamentals.
Journal of Finance, 63, 1437-1467.
Wentao Ren. (2023). Retail investors' accessibility to the internet andfirm-specific information flows: Evidence from Google's withdrawal.
International Review of Economics & Finance, 86, 402-424.
doi:10.1016/j.iref.2023.03.019
Wesley S. Chan. (2003). Stock price reaction to news and no-news: drift
and reversal after headlines. Journal of Financial Economics, 70(2),223-260. doi:10.1016/S0304-405X(03)00146-6.
Wilder, J. W. (1978). New concepts in technical trading systems.
Greensboro, N.C.: Trend Research.

Endnotes
Retail investors Sentiment data courtesy of Google Bard
(https://bard.google.com/?hl=en) and Stock charts courtesy of
StockCharts (www.stockcharts.com).

IFTA.ORG PAGE 9

IFTA JOURNAL

2024 EDITION

Multiple Regression Analysis
A Forecasting Technique for the Financial
Markets"… There are three types of lies: lies, damn lies and statistics …"
Benjamin Disraeli (1804-1881), Prime Minster of Great Britain from
1874 to 1880

Abstract
In financial markets forecasting is an essential aspect ofmaking investment and trading decisions, managing risk, or
optimizing portfolios. Accurate predictions of stock prices andreturns, bond yields, and other financial indicators can provide
valuable insights into market trends and help investors andtraders identify potentially profitable opportunities. However,
it is well known that forecasting in financial markets is a very
challenging task, as these markets are complex, dynamic, andsubject to a wide range of economic, political, and social factors.
An investor might simply want to find the strongest stock ina given sector or financial index, while a trader may want toforecast future price movements of a security based on a variety
of factors, such as economic indicators, market sentiment, orcompany-specific information. Or, she/he might need to identify
the factors influencing the risk of a particular investment toassess the impact of interest rates, currency fluctuations, orcommodity prices on the value of an asset.
Multiple regression is a statistical technique commonly usedin finance to predict the future values of financial assets. It
involves analyzing the relationship between one dependent
variable and several independent variables, and then using thisinformation to make predictions. Multiple regression models
are useful because they consider the effects of several factors
simultaneously and can provide more accurate forecasts thansimple linear models. By including a range of economic andfinancial indicators in the regression model, it is possible toidentify the factors that are most likely to impact the dependent
variable and use this insight to make informed investment andtrading decisions.
Many of these concepts are also important in technicalanalysis and should be understood by all technicians to increase
the probability of successful trades, since multiple regression
can be a useful tool to estimate the underlying price direction
for a given security.
In this work, a rigorous statistical assessment of multiple
regression is presented and a regression model to forecast the
behavior of the stock market based on financial and economic
indicators is developed and thoroughly tested by verifying thestatistical assumptions. Furthermore, statistical accuracy
metrics have been used to compare the regression model
against other forecasting techniques.

PAGE 10 IFTA.ORG

Davide Pandini, PhD, MFTA, CFTe, CMT, CSTA
Milano, Italy+39 348 397 3247
davide.pandini@hotmail.com

1. Introduction
The financial markets and the price of the asset classes
are complex systems that are influenced by a several factors,
ranging from economic and financial indicators to geopoliticalglobal events. Hence, predicting the behavior of financial
markets and asset classes is a challenging task [1], but one thatis of utmost importance to investors and traders.
Regression techniques are a widely used statistical analysis
tool and have been used extensively in financial analysis
and investment management for several years, with many
researchers finding evidence of their effectiveness in predicting
the behavior of asset prices and returns in the financial markets[2]. In [3] a trading approach based on linear regression waspresented. In this work, linear regression was considered as areliable method to represent the underlying trend of a given
security.
Multiple regression involves modeling the relationshipbetween a dependent variable (such as stock price or bondyield) and several independent variables (such as interest
rates, economic indicators, or company-specific data). By
estimating the coefficients of these independent variables,
multiple regression allows the analysts to identify the mostinfluential factors driving the movement of asset prices, and to
make predictions about future performance. This approach has
proved particularly useful in analyzing composite relationships
between financial variables and in identifying key drivers ofasset returns. For example, multiple regression analysis has
been used to study the impact of macroeconomic factors suchas inflation and interest rates on asset prices, as well as toanalyze the performance of individual securities and portfolios.
One key advantage of multiple regression is its ability toincorporate many elements into the model, allowing for a morecomprehensive understanding of the variables influencing theasset prices and the financial markets.
Despite its widespread use, however, multiple regression
analysis is not without some limitations. One challenge is thepotential for overfitting, where the model becomes too complex
and begins to fit noise rather than signal. Another challenge
is the dynamic nature of financial markets, where the factorsthat influence the asset values may change over time, making
it difficult to build a model that can accurately predict future
market and price movements. Furthermore, the techniqueassumes that the relationship between the dependent variable
and the independent variables is linear (or quite close to linear),and that data are normally distributed. In practice, theseassumptions may not hold in the financial markets, and analysts
and traders must take care to avoid the potential pitfalls ofusing multiple regression inappropriately. In order to avoid

IFTA JOURNAL

these drawbacks, a rigorous assessment of all the statisticalassumptions is mandatory.
This work presents an overview and assessment of multiple
regression forecasting for the financial markets, in particular
for the stock market represented by the S&P 500 index, basedon some interest rates, prices, and economic indicators.
Moreover, it includes a thorough discussion of its applications,benefits, and limitations.
The paper begins by describing the historical data andlookback period analyzed to develop the stock market multiple
regression model. Next, it continues by introducing the basic
principles of multiple regression analysis and explaining how
it can be applied in the financial markets. Then, it discusses
some of the key issues and challenges associated with multiple
regression, such as data quality, model specification, andinterpretation of results. Overall, this work aims to provide acomprehensive introduction to multiple regression, highlighting
its strengths and limitations, and providing guidelines on its
appropriate use in financial analysis and forecasting.
This paper is organized as follows: In Section 2, the stock
market dependent (or explained) variable and the independent(or explanatory) variables are defined through their rates,
prices, and macroeconomic areas. Next, descriptive statistics on
the historical data are calculated. Section 3 discusses multiple
regression statistics, analysis of variance or ANOVA, andcoefficients analysis.
In Section 4, multiple regression correct specification
is evaluated through the individual coefficients statisticalsignificance and corrected through backward elimination
stepwise regression. After that, multiple regression
independent variables linear independence is evaluatedby means of multicollinearity test and corrected with a
specification re-evaluation. Next, the multiple regression
correct functional form is evaluated through a linearity
test and corrected through non-linear quadratic variabletransformations. Then, multiple regression residuals
autocorrelation is evaluated and adjusted by including lagged
dependent variable data in the original regression. Later,
multiple regression residuals homoscedasticity is evaluatedand improved through heteroscedasticity consistent standard
errors estimation. Finally, multiple regression residuals
normality is assessed. It is worth noting that to maximize theeffectiveness and robustness of the multiple regression analysis

2024 EDITION

forecasting, a rigorous assessment of all the assumptions mustbe performed, to understand and evaluate the capabilities andlimitations of this statistical analysis method.
In Section 5, multiple regression forecasting accuracy isevaluated by dividing the historical data into training andtesting ranges. The training range is used for the best model
fitting by going through the steps described in the previous
Section. Next, the best fitting model coefficient values are used
to forecast the stock market behavior within the testing range.
Finally, the forecasted values accuracy in the testing range isevaluated by comparing it with random walk and arithmetic
mean benchmarks using statistical accuracy metrics. Section 6
introduces an alternative time series forecasting technique like
Exponential Triple Smoothing. This method consists of fitting a
curve to the historical data and extrapolating it into the future,assuming that the future values will follow the same pattern
as the past values, with some degree of randomness. Finally,
Section 7 presents some conclusive remarks.

2. Data Analysis and Descriptive
Statistics
To create a robust stock market (S&P 500) model that
explains the changes in S&P 500 price using economic data,
it is necessary to select the most meaningful data. Lincoln [4]suggested to use both corporate and Treasury bonds, priceindexes, and other economic indicators.
The historical data used in this work is based on more than 26
years of arithmetic monthly returns of the S&P 500 State Street
Exchange Traded Fund (ETF ticker symbol: SPY) adjusted close
prices, effective monthly yield of 1 Year U.S. Treasury Bill Yield,
10 Years U.S. Treasury Note Yield, U.S. High Yield Corporate
Bond Index Yield, arithmetic monthly inflation or deflation of
U.S. Consumer Price Index, U.S. Producer Price Index, arithmetic
monthly returns of West Texas Intermediate Oil prices,arithmetic monthly changes of U.S. Industrial Production Index
value, and U.S. Personal Consumption Expenditures amount,from January 1st, 1997, to February 1st, 2023 corresponding to
314 observations for each time series.
The historical data were downloaded from Yahoo! Finance [8]and from the Federal Reserve Economic Data (FRED) database of
economic time series, maintained by the Federal Reserve Bankof St. Louis [9], and are summarized in Table 1.

Table 1. Asset classes and data sources

IFTA.ORG PAGE 11

IFTA JOURNAL

2024 EDITION

For multiple regression forecasting, monthly data is divided
into a training range for best model fitting, and a testing range
for evaluating best fitting model forecasting accuracy. The
training range goes from January 1st,1997, to December 31st,
2012, including the first 16 years of data corresponding to 192
observations for each time series. The testing range goes fromJanuary 1st, 2013, to February 1st, 2023, with more than 10 yearsof data corresponding to 122 observations for each time series.
The S&P 500 index (i.e., stocks) is the dependent (orexplained variable) and consists of the SPY ETF adjusted close
prices arithmetic monthly returns. The eight independent(or explanatory) variables consist of rates, prices, andmacroeconomic indicators:• Rates• 1 Year Treasury (t1y) consists of effective monthly yield of
1 Year U.S. Treasury Bill bond equivalent yield or quoted
annual yield;• 10 Year Treasury (t10y) consists of effective monthly yield of
10 Year U.S. Treasury Note bond equivalent yield or quoted
annual yield;• High Yield (hyield) consists of effective monthly yield of U.S.
High Yield Corporate Bond Index equivalent yield or quoted
annual yield;• Prices• Consumer Prices (cpi) consists of U.S. Bureau of Labor
Statistics Consumer Price Index arithmetic monthly
inflation or deflation;• Producer Prices (ppi) consists of U.S. Bureau of Labor
Statistics Producer Price Index arithmetic monthly inflation
or deflation;• Oil Prices (oil) consists of U.S. Energy Information
Administration West Texas Intermediate oil prices
arithmetic monthly returns;• Macro• Industrial Production (indpro) consists of U.S. Federal
Reserve Economic Data Industrial Production Index valuearithmetic monthly change;• Consumption Expenditure (pce) consists of U.S. Bureau
of Economic Analysis Personal Consumption Expenditure
amount arithmetic monthly change.
All the variables are expressed in terms of the arithmetic
monthly returns:

2.1 Descriptive Statistics
Descriptive statistics were considered to perform an early
analysis of the dataset. The variables used for this preliminary
assessment are:• Arithmetic mean, consisting of the data average:• Standard deviation, consisting of the data amount ofdispersion or variation from its arithmetic mean:• Skewness, consisting of the data probability distribution
asymmetry from its arithmetic mean:• Zero skew indicates symmetric data probability
distribution;• Positive skew indicates data probability distribution withasymmetric tail extending towards positive values;• Negative skew indicates data probability distribution withasymmetric tail extending towards negative values;• Excess kurtosis, consisting of the data probability
distribution peakedness or flatness compared with a normal
probability distribution:• Zero excess kurtosis indicates data probability distribution
peakedness or flatness similar to a normal probability
distribution;• Positive excess kurtosis indicates data probability
distribution more peaked than a normal probability
distribution;• Negative excess kurtosis indicates data probability
distribution flatter than a normal probability distribution;

The descriptive statistics results on the complete historical
data from 1997 to 2023 of the asset classes conveyed in Table 1
are summarized in Table 2.

PAGE 12 IFTA.ORG

IFTA JOURNAL

2024 EDITION

Table 2. Descriptive statistics results

All the explanatory variables have a probability distribution
more peaked than a normal distribution, while the distribution
asymmetry is either positive or negative. Based on theseresults, the probability distributions of the independent
variables deviate from the typical shape of a normal probability
distribution.

3.Multiple Regression Analysis
Multiple regression analysis is a statistical method used
to analyze the relationship between one dependent variable(i.e., explained variable or predicted variable) and a set of
multiple independent variables (i.e., explanatory variables
or predictors). It consists of fitting the best model within the
training data range, then using the values of the best fitting
model coefficients to forecast the dependent variable value inthe testing data range and evaluating its prediction accuracy.
In other words, multiple regression analysis allows us to predict
how the changes in one or more independent variables affect thedependent variable. The output of multiple regression analysis
consists of regression statistics, analysis of variance (i.e.,
ANOVA) and regression coefficients analysis.
ANOVA is a statistical technique used to test the overallsignificance of a multiple regression model. ANOVA evaluates
whether there is a significant relationship between thedependent variable and the set of independent variables in themodel. The ANOVA table shows the variation in the dependent
variable that is explained by the independent variables, aswell as the dependent variable variation that is not explainedby the independent variables (i.e., the residual variation).
ANOVA generates the F-statistic and the associated p-value (i.e.,significance F), which are used to test the null hypothesis that all
the regression coefficients in the model are equal to zero, thus
indicating that there is no significant relationship between thedependent variable and the independent variables. If the p-valueof the F-statistic is less than the significance level (e.g., 0.05
at 95% of confidence level), then we reject the null hypothesis
and conclude that at least one of the independent variables in
the model is significantly related to the dependent variable. In
other words, the regression model as a whole is significant. It is
important to note that ANOVA only tests the overall significanceof the model and does not provide information about thestatistical significance of the individual independent variables.
To determine which independent variables are significant, weneed to examine the individual t-statistic for each regression
coefficient. In summary, ANOVA is a useful tool for assessing

the overall significance of a multiple regression model and canprovide important information about the relationship between
the dependent variable and the set of independent variables.
In this work we analyze three areas: regression statistics,
ANOVA, and regression coefficients. Although the formulasof the statistical parameters reported in this Section are wellknown and can be found in any statistical analysis textbook [5][6][7], nevertheless, they are summarized below to make thereading of this paper self-contained.
3.1
Regression Statistics
The regression statistics consist of coefficient ofdetermination, adjusted coefficient of determination, andregression standard error:• Coefficient of determination or R2 (R Square) consists of thepercentage of the variance from the dependent variable
explained by its relationship with the independent variables:• Adjusted coefficient of determination or adj R2 (Adjusted R
Square) consists of the percentage of the variance from thedependent variable explained by its relationship with theindependent variables adjusted by the degrees of freedom:• Regression standard error consists of the standard deviation
estimation of the regression residuals or forecasting errors
and is a measure of the accuracy of the regression model'spredictions. It is also known as the standard error of theestimate, and it represents the average distance that theobserved values fall from the regression line:

IFTA.ORG PAGE 13

IFTA JOURNAL

2024 EDITION

3.2 Regression Statistics Results
The regression statistics results obtained from the historical
data set reported in Table 1 for the entire backtesting period(monthly data from January 1997 to February 2023) aresummarized in Table 3.

• Total degrees of freedom consist of the number ofobservations minus the constant or intercept term, andrepresent the total variation in the dependent variable
explained by the regression model;

Table 3. Regression statistics• Regression sum of squares consist of the explained sum ofsquares, and is used in regression analysis to quantify theamount of variation in the dependent variable explained by
the independent variables;• Residuals sum of squares consists of the unexplained sum ofsquares, and quantifies the amount of unexplained variationin the dependent variable;
The multiple R parameter is a measure of the strength anddirection of the linear relationship between the dependent
variable and the set of independent variables included in
the regression model and is expressed by the relationship:
The R Square value of 0.47 reported in Table 3 means thatthe independent variables in the regression model explain 47%of the variation in the dependent variable. In other words, theR2 value of 0.47 indicates that the independent variables areable to explain a moderate amount of the variability in thedependent variable, but that there is still a significant amount ofvariation in the dependent variable that is not explained by the
independent variables in the model.
3.3 Analysis of Variance (ANOVA)
The analysis of variance, or ANOVA, consists of the following
parameters: regression degrees of freedom, residuals degrees of
freedom, regression sum of squares, residuals sum of squares,
total sum of squares, regression mean square error, residuals
mean square error, regression F-statistic, and regression
p-value (i.e., significance F):• Total sum of squares consists of the explained andunexplained sum of squares, and quantifies the total variationin the dependent variable;• Regression mean square error consists of determining the
explained regression variance, and measures the amountof variation in the dependent variable explained by the
independent variables;• Regression mean square error consists of determining the
explained regression variance, and measures the amountof variation in the dependent variable explained by the
independent variables;• Regression degrees of freedom consists of the number of
independent or explanatory variables, and is used in ANOVA
to compute the F-statistic to test the overall significance ofthe regression model;• Residuals degrees of freedom consists of the number ofobservations minus the number of regression coefficients
including the constant or intercept term, and it represents
the number of degrees of freedom associated with theunexplained error in the regression model. It is used in thecalculation of the regression standard error;

PAGE 14 IFTA.ORG• Regression F-statistic consists of determining therelationship between explained and unexplained regression
variance. The F-statistic is a single value calculated from theratio of two variances, and it is used in statistical tests suchas ANOVA to test the null hypothesis that all the regression
coefficients (except the intercept) are equal to zero, against
the alternative hypothesis that at least one of the coefficientsis different from zero. The regression F-statistic is computedby dividing the regression mean square error by the residual
mean square error. If the regression F-statistic is large
enough, it indicates that the regression model is a better
fit for the data than the null model, which assumes that all
the coefficients are zero. The significance of the F-statistic

IFTA JOURNAL

can be assessed using an F distribution with dfreg degrees
of freedom for the numerator (where dfreg is the number of
independent variables) and n-dfreg-1 degrees of freedom forthe denominator (where n is the number of observations);• Regression p-value (F-statistic p-value or significance F)
consists of determining whether regression coefficientsare jointly statistically significant. This formula is usedin regression analysis to assess the significance of the2024 EDITION

regression model. It calculates the probability of observing
an F-statistic as large as the one computed from the data,
under the assumption that the null hypothesis (all regression
coefficients are zero) is true:

3.4 ANOVA Results
The ANOVA results on the historical dataset are reported inTable 4.

Table 4. ANOVA results

The multiple regression p-value (i.e., significance F) is used to determine whether the coefficients of the independent variables in themodel are jointly statistically significant, that is, whether they have a statistically significant effect on the dependent variable. A p-valueless than 0.05 (at the 95% level of statistical confidence) indicates that the coefficients are statistically significant. This means that there isstrong evidence suggesting that the independent variables are associated with the dependent variable and that the relationship is unlikely
to have occurred by chance.
3.5 Regression Coefficients Analysis
The regression coefficients analysis consists of the following parameters: regression coefficients, standard error, t-statistic, and p-value
for each coefficient:• Regression coefficients are the values βwhich minimize the residuals sum of squares. The
SSres is a measure of the difference between the observed values of the dependent variable and the predicted values (i.e., fitted values)
from a regression model. It is used to evaluate the goodness of fit of a regression model, where a smaller SSres indicates a better fit;

• Regression coefficients standard error consists of the standard deviation estimation of regression residuals or forecasting errors for eachcoefficient;• Regression coefficients t-statistic consists of determining the relationship between coefficient value and standard error;• Regression coefficients p-value consists of determining whether regression coefficients are individually statistically significant.

IFTA.ORG PAGE 15

IFTA JOURNAL

2024 EDITION

3.6 Regression Coefficient Results
Table 5. Multiple regression coefficients

The p-values reported in Table 5 are related to the statisticalsignificance of each regression coefficient individually (while
the p-value reported in Table 4 relates to the joint statisticalsignificance of all the regression coefficients). From theindividual p-values it is possible to assess whether there aresome explanatory variables that are not statistically significant(with the p-value > 0.05) at the 95% confidence level. Therefore,
it is important to differentiate between the individual statisticalsignificance of each coefficient and the joint statisticalsignificance.

4. Multiple Regression Assumptions
The assumptions for multiple regression consist of
independent variables correct specification, independent
variables with no linear dependence, regression correctfunctional form, residuals with no autocorrelation, residuals
homoscedasticity, and residuals normality. All theseassumptions must be rigorously tested in order to have agood assessment of the regression model for an accurateinterpretation of the results.
The correct specification refers to the appropriate selectionof the explanatory variables (or independent variables) that will
be included in the regression model. The key aspect of correct
specification is to include in the model only those variables thathave a statistically significant impact on the dependent variable,
while excluding those that do not significantly contribute to
the model statistical accuracy. Including statistically irrelevant
explanatory variables in a multiple regression model can lead toseveral drawbacks, such as:• Reduced precision of coefficient estimates: statisticallyinsignificant variables may reduce the precision ofcoefficient estimates for the significant variables. This
happens because including irrelevant variables introduces
additional variability into the model, which can obscure therelationships between the explanatory variables and thedependent variable;• Increased risk of overfitting: Irrelevant variables can increase
the risk of overfitting, which occurs when a model fits thenoise in the data rather than the underlying relationships.
Overfitting leads to poor generalization performance whenthe model is applied to new data;
PAGE 16 IFTA.ORG• Increased complexity of the model: Irrelevant variables canincrease the complexity of the model without adding any
explanatory power. This can make the model more difficult tointerpret;• Potential violation of assumptions: Irrelevant variables canpotentially violate the assumptions of the model, such as
normality, linearity, and homoscedasticity. These violations
can lead to biased and unreliable coefficient estimates andstatistical inference.
It is important to consider the theoretical and empiricalevidence when selecting the independent variables forinclusion in the model. Additionally, it is essential to evaluate
the robustness of the results by performing sensitivity
analyses, such as testing the stability of the coefficients when
adding or removing variables from the model. Overall, thecorrect specification of a multiple regression model is criticalfor obtaining valid and reliable results that can be used for
informed trading and investment decisions.
Correct specification is done through a variable selection
procedure, which consists of determining the individuallyand jointly statistically significant regression coefficients
through backward elimination or forward selection stepwise
regressions:• Backward elimination stepwise regression consists ofremoving individually non-statistically significant variables
one step at a time until all variables are individually andjointly statistically significant;• Forward selection stepwise regression consists of adding
individually statistically significant variables one step
at a time while all variables are individually and jointly
statistically significant.
4.1 Correct Specification: Backward Elimination
Stepwise Regression
In this work we consider the backward elimination stepwise
regression. This method starts with a model that includes all
the independent variables, and iteratively removes the leastsignificant variable until only the most significant variables
remain in the model. At each step, the statistical significanceof each independent variable is evaluated, and the variable

IFTA JOURNAL

with the highest p-value is removed if its p-value exceeds apredefined threshold (i.e., 0.05). This process is repeated until
all remaining independent variables have p-values below thethreshold, or until there are no more variables to remove. The
final model includes only the independent variables that are
statistically significant predictors of the dependent variable.

2024 EDITION

The multiple regression coefficients of the complete model
are reported in Table 5, where the least significant explanatory
variable (with the highest p-value) is indpro, which is removed
from the model. After step 1 of the backward elimination
stepwise procedure, the remaining independent variables are
summarized in Table 6.

Table 6. Variable selection (step 1)

After step 1, the least statistically significant independent variable (with the highest p-value) is cpi, which is eliminated in step 2.
Table 7. Variable selection (step 2)

After step 2, the least statistically significant independent variable is ppi, which is eliminated in step 3.
Table 8. Variable selection (step 3)

After step 3, the least statistically significant independent variable is oil, which is eliminated in step 4.

IFTA.ORG PAGE 17

IFTA JOURNAL

2024 EDITION

Table 9. Variable selection (step 4)

After step 4, the least statistically significant independent variable is t1y, which is eliminated in step 5.
Table 10. Variable selection (step 5)

After step 5, the remaining independent variables are shown in Table 10, where all the predictors are statistically significant at the
95% confidence level. To confirm this conclusion, the ANOVA results are reported in Table 11, where the significance F value is < 0.05,
verifying that the explanatory variables in Table 10 are also jointly statistically significant with 95% confidence level.
Table 11. ANOVA results (step 5)

At this stage, the backward elimination stepwise procedure can be considered terminated, and the multiple regression model can be
expressed as:

where the regression statistics are summarized in Table 12.
Table 12. Regression statistics after step 5

According to the coefficient of determination (R Square), 46.39% of the variance in the dependent variable is explained by the
independent variables. The adjusted R Square takes into account the number of independent variables and penalizes the addition ofirrelevant or redundant independent variables in the model. Therefore, the adjusted R Square is a more appropriate measure of themodel goodness of fit when comparing models with different numbers of independent variables, and after step 5 it explains 45.87% of
the dependent variable variance. It is worth noting that by construction, adjusted R Square is always lower than R square.
To further simply the model and perform linearity, autocorrelation, and homoscedasticity tests, the backward elimination stepwise
procedure is continued to reduce the number of independent variables. After step 5, the least statistically significant independent
variable is pce, which is eliminated in step 6.
PAGE 18 IFTA.ORG

IFTA JOURNAL

2024 EDITION

Table 13. Variable selection (step 6)

The regression statistics after step 6 are reported in Table 13, and by eliminating the explanatory variable pce, there is only anegligible reduction in the model predictive power of less than 2% with respect to step 5, as reported in Table 14.
Table 14. Regression statistics after step 6

Finally, in step 7 after eliminating the independent variable t10y, the only remaining explanatory variable is hyield:

as shown in Table 15.
Table 15. Variable selection (step 7)

The regression statistics are summarized in Table 16, and the loss of the model predictive power stemming from removing the t10y
independent variable is still less than 2%.
Table 16. Regression statistics after step 7

The overall loss of predictive power from a model with three predictors (t10y, hyield, pce) shown in Table 10, to a model with only
one independent variable (hyield) is ~3%, but a simple model will allow to more easily assess other critical features such as linearity,
autocorrelation, homoscedasticity, normality.
4.2 Linear Independence
Linear independence consists of the regression explanatory variables not being highly correlated. When two or more explanatory
variables are perfectly correlated, then they are linearly dependent, and it is impossible to estimate the unique coefficients for each ofthem. This situation is known as perfect multicollinearity, and as a result, the regression model becomes unstable and unreliable. To
avoid this problem, we need to ensure that the explanatory variables are linearly independent, which means that they are not perfectly
correlated with each other. This allows us to estimate unique regression coefficients for each variable, so that the model remains stable
and reliable.
Linear independence is evaluated through the multicollinearity test, which consists of calculating the inverted correlation matrixof the independent variables and assessing whether the main diagonal values are < 10. If the main diagonal values are > 10, then thevariance of the estimated regression coefficients is inflated, thus leading to inflated standard errors, making it difficult to distinguish
IFTA.ORG PAGE 19

IFTA JOURNAL

2024 EDITION

between the effects of the different independent variables on the dependent variable. To address multicollinearity, it may be necessary
to consider dropping one or more of the correlated independent variables from the model or using techniques such as principal
component analysis (PCA) or ridge regression to reduce the impact of multicollinearity on the model estimates. The multicollinearity
test must be performed when there are two or more explanatory variables. When all the elements on the principal diagonal of thecorrelation matrix are < 10 like in Table 17, then there is no multicollinearity (or linear dependence) among the explanatory variables.
Table 17. Inverted correlation matrix

The explanatory variables are not linearly dependent and to further confirm this conclusion, the correlation matrix reported in Table
18 shows a low correlation among all the explanatory variables, except for pce vs indpro, which will not be included in the model.
Table 18. Correlation matrix

4.3 Correct Functional Form
The correct functional form consists of evaluating whether
the optimal relationship among the regression independent
variables with the dependent variable is linear or non-linear.
One common approach to selecting the correct functional form
is to begin with a simple linear regression model and then testfor deviations from linearity using various diagnostic tools.
For example, we can use residual plots, scatterplots, or tests oflinearity. If there is evidence of non-linearity, we can consider
using polynomial regression, logarithmic transformation,or other functional forms that better capture the shape ofthe relationship between the dependent variables and the
independent variables.
The Ramsey RESET (Regression Equation Specification
Error Test) linearity test [10] consists of adding squared fitted
regression data as independent variable, and assessing if it isindividually statistically significant. The test was developed

PAGE 20 IFTA.ORG

by the economist James Ramsey in 1969 and is based on theidea that if a regression model is correctly specified, then any
function of the independent variables (such as their squared
or cubed values) should not have a significant impact on thedependent variable. In contrast, when such a function isfound to be significant, this suggests that the model may be
misspecified. The RESET test involves adding a set of squared(or cubed) terms of the original independent variables to theregression model and then examining whether these new terms
are statistically significant. If they are significant, then themodel may be misspecified, and it should be considered adding
additional variables to the model. Overall, the RESET test is a
useful tool for identifying potential problems with a regression
model and for improving its accuracy. If the squared fitted
regression coefficient is individually statistically significant,then non-linear functional form transformations of dependent
and/or independent variables need to be evaluated.

IFTA JOURNAL

2024 EDITION

A quadratic functional form consists of performing a quadratic transformation to the independent variables:

In the Ramsey RESET linearity test we evaluate if the addition of the squared fitted values independent variable, computed with themodel obtained after variable selection step 7 represented in Table 15.

has a p-value > 0.05. The model evaluated in the RESET test is given by:
and the regression results are reported in Table 19.
Table 19. Ramsey RESET linearity test regression results

Since the p-value of the squared fitted independent variable is < 0.5, this variable is statistically significant at the 95% confidence
level, thus indicating that the model obtained after variable selection step 7 may be misspecified, and that a liner form might not
be the best predictive model. Moreover, the ANOVA results shown in Table 20 report that the significance F is < 0.05, confirmingthat the coefficients are jointly statistically significant. In the Ramsey RESET linearity test, the null hypothesis is that the multiple
regression model is correctly specified with respect to linearity, meaning that there is no omitted non-linear relationship between
the independent variables and the dependent variable. In other words, the null hypothesis states that the functional form of theregression model is correctly specified and that there is no need to include additional non-linear terms. The alternative hypothesisis that the model is misspecified, and that there is a need to include additional non-linear terms to better capture the relationshipbetween the independent variables and the dependent variable. A significance F < 0.05 rejects the null hypothesis.
Table 20. Ramsey RESET linearity test ANOVA results

The results of the RESET test suggest that there is evidence of non-linearity in the relationship between the dependent variable
and the independent variables in the regression model. Hence, a non-linear functional form transformation of the dependent andindependent variables, like a quadratic transformation, needs to be evaluated.
4.4 Residuals No Autocorrelation
Residuals autocorrelation occurs when the forecasting errors (or residuals) of a regression model are not statistically independentand are correlated with each other. The residuals no autocorrelation test consists of evaluating whether the residuals (or forecastingerrors) have a constant mean value through the Breusch-Godfrey autocorrelation test [11][12], also known as the Breusch-Godfrey LM(Lagrange Multiplier) test, which is a statistical test used to detect the presence of autocorrelation in a regression model.
The test checks whether the residuals are significantly correlated with their lagged values, thus indicating the presence ofautocorrelation. It consists of considering the regression residuals data as the dependent variable, then adding the lagged regression
residuals data as independent variables and assessing if they are individually or jointly statistically significant. The Breusch-Godfrey
autocorrelation test verifies the null hypothesis that there is no autocorrelation in the residuals of a regression model. Specifically,

IFTA.ORG PAGE 21

IFTA JOURNAL

2024 EDITION

the null hypothesis states that the residuals of the regression model are not correlated with each other over time or across different
observations. The test is performed by:• Estimating the residuals of the regression model;• Using these residuals to construct an auxiliary multiple regression equation;• The auxiliary regression equation includes the lagged values of the residuals as explanatory variables;• The null hypothesis states there is no significant autocorrelation in the residuals of the auxiliary regression equation over time oracross different observations;• The test statistic for the Breusch-Godfrey autocorrelation test is the LM (i.e., Lagrange Multiplier) test statistic, which measures thedifference in the sum of squared residuals between the null and alternative hypotheses;• The LM-statistic follows a chi-squared distribution with the number of lagged residuals used as degrees of freedom;• If the calculated LM-statistic is greater than the critical value at the desired level of statistical significance, the null hypothesis of no
autocorrelation is rejected, and the alternative hypothesis of autocorrelation is accepted.
The Breusch-Godfrey autocorrelation test is commonly used in econometric analysis to test for autocorrelation in time series.
The test can be applied to both linear and nonlinear regression models, and it can be used to test for autocorrelation up to a specified
number of lags.
The current period, previously fitted model forecasting errors or residuals are given by the following expression:
where x(i,t) is the i-th explanatory variable at timeis the previously fitted model forecasting error or residual at period t-p, p
is the number of lags included in the test, and et is the regression forecasting error or residual at time t. If indicates that we include
only 1 lag, and indicates we include p lags, then we evaluate the ,...,γ joint statistical significance by testing if either theirt-statistic or F-statistic p-value (i.e., significance F) is < 0.05:

If lagged regression residuals coefficients ,...,γ are individually or jointly statistically significant, then lagged dependent
variables data needs to be added as independent variables in the original regression model. Therefore, we have that the current period
regression fitted or forecasted values (in case of 2 explanatory variables and p-lagged residuals) are given by:where AR1,...,ARp are the autoregressive coefficients multiplied by the previous period dependent or explained variable data all theway to the p autoregressive coefficients plus the regression forecasting error or residual at time t.
We performed the Breusch-Godfrey test including only 1-lagged (or the previous period) residuals. As dependent variables weconsider the corresponding regression fitted values forecasting errors or residuals, and as independent variables we have the same
variables included in the corresponding model (i.e., hyield) and the previous period residuals. The regression results are reported inTable 21.
Table 21. Breusch-Godfrey test regression results

The p-value of the lagged residuals is > 0.05 showing that the 1-lagged residuals independent variable is not statistically significant;therefore, we can conclude there is no 1-lagged residuals autocorrelation with 95% of statistical confidence. Moreover, the F-statistics
p-value (i.e., significance F) reported in Table 22 confirms that the 1-lagged residuals are not jointly statistically significant.

PAGE 22 IFTA.ORG

IFTA JOURNAL

2024 EDITION

Table 22. Breusch-Godfrey test ANOVA results

In conclusion, there is no need to add lagged dependent
variables data in the original multiple regression model.
4.5 Residuals Homoscedasticity
Residuals homoscedasticity consists of evaluating whether
the regression residuals or forecasting errors have a constantvariance. Two main homoscedasticity tests can be performed:• Breusch-Pagan test [14]: This is a statistical test that checks
whether the variance of the residuals is constant acrossall levels of the independent variables. The null hypothesisof the test is that the variance of the residuals is constant(homoscedastic). If the p-value is less than the significancelevel (i.e., 0.05 at 95% of statistical confidence), then the null
hypothesis is rejected, indicating that the assumption ofhomoscedasticity does not hold;• White test [13]: This test is similar to the Breusch-Pagan
test but is more robust to violations of normality andhomoscedasticity. The test checks whether the residuals areuncorrelated with the squared values of the independent
variables. If the significance F value is < 0.05, then thenull hypothesis of homoscedasticity is rejected at 95% ofstatistical confidence.
In this work we performed the White test, which is commonlyused to test for heteroscedasticity in regression analysis. It was
proposed by Halbert White in 1980 and is sometimes referred
to as the “generalized heteroscedasticity test”. The White test isa robust version of the Breusch-Pagan test, which assumes thatthe errors in the regression model are normally distributed. In
contrast, the White test is more general as it can be used whenthe errors are not normally distributed. The test is based on thefollowing steps:• Obtain the multiple regression model residuals;• Square the residuals to obtain the new dependent variable;• Estimate a new regression model using the squared residuals

as dependent variable and the independent variables andtheir squared values as additional independent variables;• Test the null hypothesis that the coefficients of the squared
independent variables are equal to zero, thus indicatinghomoscedasticity.
There are two versions of the White homoscedasticity test:
the White(no-cross terms) and the White(cross terms) tests,
which consist of using squared regression residuals data as
dependent variable and doing quadratic (no-cross terms) or
quadratic and cross products (cross terms) transformations
to the independent variables in order to assess if the squared
independent variables are jointly statistically significant. If
the independent variables are jointly statistically significant,heteroscedasticity consistent standard errors estimation needs
to be done (and the null hypothesis of homoscedasticity must be
rejected).
In this work we performed the White(no-cross terms) test.
The following regression model is an example of the White(nocross terms) homoscedasticity test with two independent or
explanatory variables, in which the current period, previously
fitted model squared residuals (to the power of two) are
expressed by the following formula:
For this test the regression explained variable is the squared
residuals and the independent variables are the quadratictransformation of the explanatory variables. The residuals
homoscedasticity (or constant variance) is evaluated bymeans of the regression F-statistic p-value (significance F). If
the significance F is < 0.05, meaning that the independent or
explanatory variables are jointly statistically significant, thenwe need to reject the null hypothesis (homoscedasticity of theresiduals), the heteroscedasticity (i.e., non-constant variance)of the residuals cannot be rejected, and we conclude that theresiduals are heteroscedastic.

Table 23. White(no-cross terms) homoscedasticity test ANOVA results

In Table 23 the significance F value is < 0.05, therefore the corresponding regression residuals are not homoscedastic. The residuals
are heteroscedastic with 95% of statistical confidence according to the White(no-cross terms) test. Hence, it is necessary to perform
an estimation of heteroscedasticity consistent standard errors and the associated F-statistic. Moreover, the p-values of the White(no-IFTA.ORG PAGE 23

IFTA JOURNAL

2024 EDITION

cross term) test regression results shown in Table 24 confirm that regression coefficients of the linear and squared independent
variables are not statistically significant with a 95% of statistical confidence.
Table 24. White(no-cross terms) homoscedasticity test regression results

4.6 Heteroscedasticity Consistent Standard Errors
Heteroscedasticity consistent (HC) standard errors (also known as robust standard errors) is a method to adjust the standard
errors in regression analysis to account for possible heteroscedasticity in the data. Heteroscedasticity means that the variance of theresiduals is not constant across all levels of the independent variables.
HC standard errors use a different method to estimate the standard errors that does not rely on the assumption of homoscedasticity.
Instead, it is based on the variance-covariance matrix of the coefficients using a sandwich estimator, which takes into account possible
heteroscedasticity. This approach leads to standard errors that are robust to heteroscedasticity, thus producing more accurateinference in the presence of heteroscedasticity. The sandwich estimator involves sandwiching the original estimator of the standard
errors between two estimates of the variance-covariance matrix. This generates a robust estimator of the variance-covariancematrix, which can then be used to calculate HC standard errors. The sandwich estimator is a popular method for estimating HC
standard errors because it is relatively simple to calculate and is robust to violations of the homoscedasticity assumption. This method
is commonly used in regression analysis and is an important tool for conducting reliable statistical inference.
In the previous section we evaluated the residuals homoscedasticity by means of the White(no-cross terms) test. In Table 23
we observed that the F-statistic associated p-value (i.e., significance F) was < 0.05, and we concluded that those residuals were
not homoscedastic, but were heteroscedastic with 95% of statistical confidence, thus highlighting the need to estimate theheteroscedasticity consistent (HC) standard errors. The HC standard errors obtained with a sandwich estimator are reported inTable 25.
Table 25. Heteroscedasticity consistent standard errors

After estimating the HC standard errors, we can estimate the HC standard errors F-statistic, which is reported in Table 26.
Table 26. Heteroscedasticity consistent standard errors F-statistic

We can compare the HC standard errors and F-statistic values with the values from the original step 7 regression model summarizedin Table 27 and Table 28 respectively
Table 27. Step 7 regression results

PAGE 24 IFTA.ORG

IFTA JOURNAL

2024 EDITION

Table 28. Step 7 ANOVA results

The HC standard errors t-statistic is computed in Table 30 as the regression coefficients divided by the HC standard errors reported
in Table 25, then the p-values are calculated as the two-tails t distribution of the absolute value of the t-statistic with the residual
degrees of freedom reported in Table 29.
Table 29. HC standard errors ANOVA results

Table 30. HC standard errors regression results

The HC standard errors p-value (i.e., significance F) in Table
29 is computed through the F distribution of the F-statistic, theregression degrees of freedom, and the residuals degrees of
freedom given in Table 29. The original regression F-statistic in
Table 28 is compared with the F-statistic in Table 29 obtainedwith the HC standard errors.
The regression p-value (i.e., significance F) in Table 28 is <0.05 and since we only have one independent variable (Table27), it is used to evaluate whether the regression that includes
that explanatory variable is a better fit than the one that only
includes the constant or intercept term. Since the p-values is< 0.05, we conclude that the regression with the explanatory
variable is a better fit with 95% of statistical confidence.
We confirm this result with the HC standard errors regressionin Table 29, where the p-value (i.e., significance F) is < 0.05, andthe regression with the independent variable is a better fit thanthe one that only includes the constant or intercept term with
a 95% of statistical confidence. The HC standard errors in Table
30 are modified with respect to the original standard errors
reported in Table 27. The HC standard errors regression p-valueof the hyield explanatory variable is < 0.05, thus confirming thatthe hyield independent variable is statistically significant with
95% of statistical confidence.
4.7 Residuals Normality
Residuals normality consists of evaluating whether the
regression residuals or forecasting errors skewness andkurtosis match a normal distribution. This is evaluated throughthe Jarque-Bera normality test [15], which is a statistical
test used to determine if a given dataset follows a normal
distribution. The Jarque-Bera test consists of calculating thetest statistic and assessing if its value is less than six. If the test
statistic value is greater than six, the dataset does not comply
with the normality assumption. The Jarque-Bera normality test
was introduced by Jarque and Bera in 1980 and is based on theidea that if a dataset is normally distributed, then its skewness
and kurtosis should match the theoretical values of 0 and 3
respectively. Skewness is a measure of the asymmetry of thedataset, while kurtosis measures the degree of peakedness ofthe distribution. The Jarque-Bera test uses the JB test statistic,
which follows a chi-squared distribution with two degrees of
freedom under the null hypothesis of normality:

where n is the sample size of the forecasting errors or
residuals, s is the skewness of the dataset, and ek is theexcessive kurtosis. To perform the test, the JB test statistic is
computed and compared against the critical value of the chisquared distribution. If the JB test statistic is greater than thecritical value (i.e., six), then the null hypothesis of normality is
rejected, indicating that the dataset does not follow a normal
distribution. If JB value is less than or equal to the critical value,
the null hypothesis of normality cannot be rejected. As shownin Table 31, the p-value from the chi-squared distribution withtwo degrees of freedom of the JB test statistic is < 0.05, then thenull hypothesis of normality is rejected with 95% of statisticalconfidence. The Jarque-Bera test results on the forecastingerrors or residuals of the step 7 regression analysis are
summarized in Table 31, and confirm that the residuals do notfollow a normal distribution.

IFTA.ORG PAGE 25

IFTA JOURNAL

2024 EDITION

Table 31. Jarque-Bera normality test results

The Jarque-Bera test is widely used in finance and economics to test the normality of financial and economic data. However, it
should be noted that the test can sometimes give false positives or false negatives, especially for small sample sizes. The Jarque-Beratest is sensitive to sample size, and the trustworthiness of the test increases with larger sample sizes. Additionally, the test may not
be appropriate for small sample sizes or non-normal distributions with heavy tails. Overall, the Jarque-Bera test is a useful tool forassessing the normality of a dataset, but it should be used in conjunction with other diagnostic tests to ensure accurate results.
4.8 Multiple Regression Assumptions Summary
All the multiple regression assumptions have been thoroughly evaluated on the complete historical data set of the independent
variables, after a correct regression model has been obtained by means of the backward elimination stepwise regression. In summary:• The explanatory variables are linearly independent and there is no multicollinearity;• The correct functional form of the regression model was estimated through the Ramsey test, and the results suggested that thereis evidence of non-linearity in the relationship among the independent variables and the dependent variable. Hence, a quadratictransformation of the explanatory variables was considered;• The residuals autocorrelation was analyzed with the Breusch-Godfrey test, whose results demonstrated there is no statisticallysignificant residuals autocorrelation and no need to add lagged dependent variables data in the original multiple regression model;• The White(no-cross terms) test demonstrated that the residuals are heteroscedastic (with no constant variance across all levelsof the explanatory variables). In this case the estimated standard errors of the regression coefficients can become biased andinconsistent;• The heteroscedasticity consistent (HC) standard errors procedure used a different method to estimate the standard errors andconfirmed that the independent variables coefficients in the original regression model are statistically significant;• The normality of the residuals was evaluated through the Jarque-Bera test. The results confirmed that the residuals do not follow anormal distribution.

5. Multiple Regression Forecasting and Results
Multiple regression forecasting consists of fitting the best model within the training data subset and using the best fitting model toforecast within the testing data subset. Forecasting can be classified into:• Ex-ante forecasting consists of dependent or explained variable current period forecast using previous periods independent or
explanatory variables data only:• Ex-post forecasting consists of dependent or explained variable current period forecast using current period independent or
explanatory variables data:

Ex-ante forecasting in multiple regression refers to predicting the values of the dependent variable before the data is collected,
based on the values of the previous period independent variables. In other words, it involves using a multiple regression model tomake predictions about future values of the dependent variable. In contrast, ex-post forecasting refers to predicting the values of thedependent variable based on the actual values of the independent variables. In other words, it involves using multiple regression topredict the values of the dependent variable after the data has been made available.
These predictions can be compared to the actual values of the dependent variable to evaluate the accuracy of the model. Ex-ante
forecasting allows to anticipate future outcomes based on current data. This can be particularly valuable in finance, where investors
and traders need to make predictions about future trends and performance. However, it is important to note that ex-ante forecasts
are inherently less accurate than ex-post forecasts, which are obtained by using actual data. This is because ex-ante forecasts are
based on assumptions about future trends and relationships between the independent and dependent variables, which may not holdtrue in practice.
In this work we perform ex-ante forecasting based on 1-lagged explanatory or independent variables.

PAGE 26 IFTA.ORG

IFTA JOURNAL

2024 EDITION

5.1 Training and Testing Range
The historical monthly data range is divided into:• Training range spanning the period from Jan 1997 till Dec 2012;• Testing range spanning the period from Jan 2013 till Feb 2023.
Multiple regression best fitting model evaluation is first performed on the training range, by obtaining the best fitted model andevaluating all the assumptions analyzed in Section 4. The forecasting accuracy of the model is then assessed on the testing range.
5.2 Forecasting Model Correct Specification (in the Training Range)
In this Section the best fitting of the regression model within the training range is performed to evaluate all the multiple regression
assumptions studied in Section 4. The initial regression model includes all the independent or explanatory variables, and the ANOVA
and regression results are shown in Table 32.
Table 32. ANOVA and regression results

In Table 32 the regression coefficient with the least statistically significant (i.e., largest) p-value is the lagged oil (loil) independent
variable, which is not statistically significant with 95% of statistical confidence. For the model correct specification, we need toperform variable selection by removing the least statistically significant explanatory variables one at a time until all the remaining
independent variables are individually and jointly statistically significant (i.e., with their p-value < 0.05) with 95% of statisticalconfidence. Therefore, we remove loil independent variable and the variable selection step 1 results are reported in Table 33.
Table 33. Variable selection (step 1) ANOVA and regression results

After variable selection step1, the least statistically significant dependent variable with the highest p-value is lt10y which is removed
from the regression model. The variable selection step 2 results are reported in Table 34, where the least statistically significant
dependent variable with the highest p-value is lpce, which is removed from the regression model.

IFTA.ORG PAGE 27

IFTA JOURNAL

2024 EDITION

Table 34. Variable selection (step 2) ANOVA and regression results

The variable selection step 3 results are reported in Table 35, where the least statistically significant dependent variable with thehighest p-value is lt1y, which is removed from the regression model.
Table 35. Variable selection (step 3) ANOVA and regression results

The variable selection step 4 results are reported in Table 36, where the least statistically significant dependent variable with thehighest p-value is lcpi, which is removed from the regression model.
Table 36. Variable selection (step 4) ANOVA and regression results

The variable selection step 5 results are reported in Table 37, where the least statistically significant dependent variable with thehighest p-value is lppi, which is removed from the regression model.

PAGE 28 IFTA.ORG

IFTA JOURNAL

2024 EDITION

Table 37. Variable selection (step 5) ANOVA and regression results

The variable selection step 6 results are reported in Table 38, where the least statistically significant dependent variable with thehighest p-value is hyield, which is removed from the regression model.
Table 38. Variable selection (step 6) ANOVA and regression results

The variable selection step 7 results are reported in Table 39, where the explanatory variable lindpro is statistically significant (i.e.,p-value < 0.05) with 95% of statistical confidence.
Table 39. Variable selection (step 7) ANOVA and regression results

Since after step 7 the regression model consists of only one explanatory variable lindpro, the ANOVA F-statistic and the associatedp-value (i.e., significance F) is < 0.05, and confirms that the regression model that includes the independent variable lindpro is a better
fit than the one that only includes the intercept term:

5.3 Forecasting Correct Specification
The correct functional form for this multiple regression forecasting consists of only one explanatory variable (i.e., lindpro)
as summarized in Table 39. Hence, in this case we do not need to verify the linear independence or multicollinearity among theindependent variables because there is only one explanatory variable.

IFTA.ORG PAGE 29

IFTA JOURNAL

2024 EDITION

We need to check the correct functional form through the Ramsey RESET linearity test, by including in the regression model thecorresponding squared fitted values from variable selection step 7 model:

The results of the Ramsey RESET linearity test are reported in Table 40.
Table 40. Ramsey RESET linearity test results

The p-value of the squared fitted values independent variable is < 0.05, hence, it is statistically significant with 95% of statisticalconfidence, and we can conclude through the RESET test that there is no linearity. Moreover, the significance F value is < 0.05, thus
rejecting the null hypothesis that there is no need of non-linear terms, in favor of the alternative hypothesis that it is necessary
to include additional non-linear terms to better capture the relationship between the independent variables and the dependent
variable. Therefore, we need a non-linear functional form of the regression model. We consider the quadratic transformation for the
independent or explanatory variable lindpro (the lagged industrial production index) as shown in the following expression:

The results of the multiple regression on the non-linear model are reported in Table 41.
Table 41. Non-linear functional form regression results

The squared lagged lindpro explanatory variable (lindpro2) has a p-value < 0.05 and it is statistically significant with 95% ofstatistical confidence. Since the linear lagged lindpro independent variable has a p-value > 0.05, then it is not statistically significant.
However, it is worth noting that even if the linear variable is not statistically significant and the quadratic form of the explanatory
variable is statistically significant, nevertheless, because of the hierarchy principle, we can include also the lagged linear variable
lindpro together with its quadratic transformation lindpro2, so that we have the complete quadratic form.
The hierarchy principle in quadratic transformation refers to the idea that when creating a quadratic regression model, the inclusionof predictor variables should be guided by a hierarchical order reflecting the relationship between the variables. In a quadratic
regression model, a quadratic term is added to the linear term of the predictor variable. The quadratic term is used to capture the nonlinear relationship between the predictor variable and the dependent variable, and the hierarchy principle suggests that the quadraticterm should be added to the model after the linear term. Moreover, the ANOVA F-statistic p-value (i.e., significance F) in Table 41
confirms that the linear and quadratic transformation of the explanatory variable are jointly statistically significant.

PAGE 30 IFTA.ORG

IFTA JOURNAL

2024 EDITION

In order to test the non-linearity through the RESET test, we include in the model the fitted values of the squared non-linear
regression represented in Table 41.

The squared fitted values explanatory variable of the non-linear regression of Table 42 has a p-value > 0.05, hence; is not statisticallysignificant with 95% of statistical confidence.
Table 42. Ramsey RESET linear test results

Therefore, we can conclude that there is linearity through the Ramsey RESET linearity test, hence, there is no need to include
further functional transformation in the quadratic model represented in Table 41:

5.4 Forecasting Residuals No Autocorrelation
We consider the non-linear regression model represented in Table 41 and its residuals or forecasting errors. The residuals
autocorrelation is evaluated by means of the Breusch-Godfrey autocorrelation test. The fitted residuals or forecasting errors from thenon-linear regression model represented in Table 41 are given by:
The dependent variable is given by the fitted residuals, while the independent or explanatory variables are given by the linear andquadratic transformation of the lagged indpro variable (lindpro) and by the lagged fitted residuals or forecasting errors:
The results of Breusch-Godfrey autocorrelation test are summarized in Table 43. The evaluation of the Breusch-Godfrey test is
performed for 1-lagged explanatory variables and the p-values of the fitted lagged residuals is > 0.05. We can conclude that there is no1-lagged residuals autocorrelation with 95% of statistical confidence. Furthermore, the significance F value obtained from ANOVA is >0.05, thus confirming that the null hypothesis cannot be rejected. The null hypothesis of the Breusch-Godfrey autocorrelation test in
multiple regression is that there is no autocorrelation in the residuals of the regression model.
Table 43. Breusch-Godfrey no autocorrelation test results

IFTA.ORG PAGE 31

IFTA JOURNAL

2024 EDITION

5.5 Forecasting Residuals Homoscedasticity
The residuals homoscedasticity has been evaluated through the White(no-cross terms) test. A quadratic transformation of thequadratic independent variable of the non-linear regression model described in Table 41 is applied. The following regression model isan example of the White(no-cross terms) homoscedasticity test with the two independent or explanatory variables of the non-linear
regression model in which the current period, previously fitted model squared forecasting errors or residuals (to the power of two) are
expressed by the following formula:
We consider the F-statistic and its corresponding p-value (significance F) reported in Table 44. The results show that the significanceF value is > 0.05, therefore we can conclude that the residuals are homoscedastic through the White(no-cross terms) test with 95% ofstatistical confidence. In fact, if the significance F is > 0.05, we cannot reject the null hypothesis, and the null hypothesis of the White
test for heteroscedasticity is that the residuals, or forecasting errors, are homoscedastic, meaning that the variances of the errors
are equal across all levels of the independent variables. More specifically, the null hypothesis of the White test affirms that there is noheteroscedasticity that can be explained by including the squared terms of the independent variables in the regression model. The test
checks whether the squared residuals from the multiple regression model are linearly related to the independent variables and theirinteractions. If the test fails to reject the null hypothesis, it suggests that the assumption of homoscedasticity is not violated, and theerrors are equally variable across all levels of the independent variables.
Table 44. White(no-cross terms) homoscedasticity test

5.6 Forecasting Residuals Normality
The residuals normality is evaluated through the Jarque-Bera normality test. The results are summarized in Table 45. The JB test
statistic is < 6, therefore we can conclude that the residuals from the non-linear functional form of the multiple regression have askewness and excess kurtosis similar to that of a normal probability distribution with 95% of statistical confidence. The p-value > 0.05
confirms that the null hypothesis, i.e., the residuals or forecasting errors are normally distributed, cannot be rejected.
Table 45. Jarque-Bera normality test results

5.7 Forecasting Accuracy Metrics and Results (in the Testing Range)
Multiple regression forecasting accuracy consists of comparing multiple regression forecasting accuracy within the testing datasubset with testing data subset random walk and training data subset arithmetic mean benchmarks, through the metrics of Mean
Absolute Error (MAE), Root Mean Square Error (RMSE), and Mean Absolute Percentage Error (MAPE).
• Mean Absolute Error consists of scale-dependent measure of forecasting accuracy based on arithmetic mean of absolute value ofresiduals or forecasting errors:

PAGE 32 IFTA.ORG

IFTA JOURNAL

2024 EDITION

where the residuals or forecasting errors are expressed as:
andare the forecasted or fitted values;• Root Mean Squared Error consists of scale-dependent measure of forecasting accuracy based on square root of arithmetic mean ofsquared residuals or forecasting errors;• Mean Absolute Percentage Error consists of scale-independent measure of forecasting accuracy based on arithmetic mean ofabsolute value of residuals or forecasting errors as percentage of actual data:

A scale-dependent measure of forecasting accuracy, such as Mean Absolute Error (MAE), is sensitive to the units of measurement
used for the target variable. For example, if the target variable is measured in dollars, the MAE will also be measured in dollars. Thismeans that the MAE value is difficult to compare between datasets or models that use different scales or units of measurement. To
address this issue, scale-independent measures of forecasting accuracy, such as the Mean Absolute Percentage Error (MAPE), are often
used. These metrics express the forecasting error as a percentage of the actual value, making them comparable across different scales
and units of measurement.
The forecasting accuracy metrics are evaluated within the testing range (from Jan 2013 till Feb 2023). The non-linear multiple
regression model to estimate the stock market returns in the testing range is expressed by:where the regression coefficients are reported in Table 41.
The benchmarks considered to evaluate the multiple regression model (i.e., MODEL) are the random walk (i.e., RANDOM WALK)
and the arithmetic mean (i.e., MEAN) in Table 46. The random walk is implemented by using the previous period stocks data plus somerandomness [16]. Among the three models, MEAN shows the smallest values for all the metrics, while MODEL has higher MAE and
RMSE than RANDOM WALK, but MAPE is smaller than RANDOM WALK. Hence, according to the scale-dependent forecasting metrics,
the random walk has a better forecasting accuracy with respect to the non-linear multiple regression model, but according to thescale-independent metric, the multiple regression model shows a better accuracy than the random walk model.
Table 46. Forecasting accuracy (testing range)

Figure 1 shows the stock market (S&P 500) forecasted returns computed with the non-linear multiple regression fitted model fromJan 2013 till Jan 2020, compared against the actual data and the random walk model.

IFTA.ORG PAGE 33

IFTA JOURNAL

2024 EDITION

Figure 1. Testing range: Jan 2013 – Jan 2020

Figure 2 shows the same data and models from Feb 2020 till Feb 2023. The negative spike in the fitted multiple regression model
is a consequence of the corresponding large drop in the industrial production index macroeconomic indicator, where in Apr 2020 theindpro return plunged by 13.38%.
Figure 2. Testing range: Feb 2020 – Feb 2023

6. Beyond Multiple Regression:
Exponential Triple Smoothing
In the previous Sections we have presented a rigorous
statistical assessment of multiple regression and havedeveloped a non-linear (i.e., quadratic) model to forecast thestock market behavior (represented by the S&P 500 index)
based on the industrial production index explanatory variable.
However, multiple regression is not the only approach that canbe used to perform predictions.
Exponential Triple Smoothing (ETS) [17][18] is a popular timeseries forecasting method that uses exponential smoothing
to predict future values based on past observations. It isparticularly useful for datasets with trend, seasonality, andrandomness, making it a valuable technique for a wide range
of applications, such as sales forecasting and stock market
analysis. Typically, trend, seasonality, and randomness are
the three key components of a time series. The trend refers
to the overall direction of the data, whether it is increasing,decreasing, or remaining constant over time. The seasonality
reflects the regular patterns or cycles in the data, which could
be daily, weekly, monthly, or yearly, and it could be influenced by
PAGE 34 IFTA.ORG

factors such as economic cycles, corporate earnings, fiscal andmonetary policies, geopolitical events, and investor behavior.
The randomness represents the unpredictable fluctuations thatare not explained by trend or seasonality, which could be caused
by unexpected news, investor sentiment, market psychology,
algorithmic trading, and technical factors like market liquidity,
trading volume, bid-ask spreads, or measurement errors.
ETS uses exponential smoothing to estimate the values of thethree components and forecast future values based on theseestimates. Exponential smoothing is a weighted average methodthat assigns different weights to the past observations basedon their recentness. The closer an observation is to the present,
the higher the weight assigned to it, and the farther away it is,
the lower the weight. This means that recent observations havemore impact on the forecast than older ones, reflecting theconcept that more recent data is more relevant to predict the
future. ETS is particularly useful when dealing with time series
data with a complex seasonal pattern or where the trend is not
linear. It can also handle data with missing values or irregularintervals between the observations.
In comparison, multiple regression is a statistical techniquethat models the relationship between a dependent variable andIFTA JOURNAL

several independent variables. Unlike ETS, multiple regression
does not take into account time series components such as trend
and seasonality.
Overall, ETS and multiple regression are two different
approaches to forecasting, and the choice between them
depends on the specific characteristics of the data being
analyzed. If the data has a strong temporal pattern, ETS may be
the more appropriate choice. However, if the data has a more
complex set of explanatory variables, multiple regression may
yield a better solution.
• Pros of Exponential Triple Smoothing:• ETS can handle time series data with complex patterns,
such as seasonality, trend, and noise (randomness).
• ETS can handle missing data and irregular time intervals,
making it a more flexible tool than (multiple) regression
analysis.
• Cons of Exponential Triple Smoothing:• ETS assumes that the underlying patterns in the time series
data are stable over time, which may not be the case whensudden changes in the underlying time series occur.
• ETS relies on the most recent observations in the data,
which can make the forecasts more volatile and less reliable
when the data is highly erratic or there is a lot of noise in thedata.
• ETS does not account for external factors that may
influence the time series data, such as economic trends.
• ETS is primarily a univariate method, meaning it only
considers one variable at a time, which may not be sufficientfor complex forecasting tasks.
• Pros of Multiple Regression:• Multiple regression can handle a wide range of independent
variables, making it useful for forecasting complex
relationships between variables.
• Multiple regression can account for external factors that
may influence the dependent variable, making it a morerobust forecasting tool in some contexts.
• Multiple regression can handle both continuous andcategorical variables, making it a more versatile tool thanETS.
• Multiple regression can provide estimates of the effect ofeach independent variable on the dependent variable, which
can be useful for interpreting the results.
• Cons of Multiple Regression:• Multiple regression assumes a linear relationship between
the independent and dependent variables, which may notalways be the case.
• Multiple regression assumes that the independent variables
are not highly correlated with each other, which can lead tobiased estimates if this assumption is violated.
• Multiple regression can be sensitive to outliers and missingdata.

2024 EDITION

6.1 Forecasting with ETSETS is a method of time series forecasting that does not use
external predictors. It is a univariate technique that relies on
the historical observations of the time series itself to makepredictions about future values. The method uses a combinationof smoothing parameters to estimate the current level, trend,and seasonal components of the time series. These estimates arethen used to forecast future values of the time series. However,this approach does not take into account any external variables
or predictors that may influence the time series.
We have used the same training range for the stocks timeseries (from Jan 1997 till Dec 2012) to train the ETS model. The
results of ETS on the testing range (from Jan 2013 till Feb 2023)
are shown in Figure 3, where along with the forecast, also the
95% upper and lower confidence bounds are represented, where
there is a 95% probability that the actual value will fall withinthese confidence bounds.
Figure 3. ETS on stocks (training and testing ranges)

A more detailed representation of ETS forecast in thetesting range is shown in Figure 4 and Figure 5. In this case thenon-linear multiple regression fitted model provides a better
forecast than the ETS model. The ETS model 95% confidencebounds yield a useful reference for the range where thepredicted variable could fluctuate.
Figure 4. ETS vs non-linear regression: testing range Jan
2013 ‒ Jan 2020

In summary, ETS is a useful method for forecasting timeseries data with complex patterns, while multiple regression is amore robust method that can handle a wider range of variables
and relationships among them.

IFTA.ORG PAGE 35

IFTA JOURNAL

2024 EDITION

Figure 5. ETS vs non-linear regression: testing range Feb
2020 ‒ Feb 2023

The accuracy metrics values of ETS forecasting are reported
in Table 47. Based on these results, multiple regression isa better method than Exponential Triple Smoothing for aqualitative forecasting of the stock market.
Table 47. ETS Forecasting accuracy (testing range)

7. Conclusions
Forecasting the stock market is a highly complex anddynamic task requiring a deep understanding of economic andfinancial factors. Both multiple regression and exponential
smoothing are commonly used techniques for forecasting, but
the choice of the best model depends on various factors such asdata availability, quality, and the specific characteristics of thedata being analyzed.
Multiple regression is typically used to identify a relationshipbetween several independent variables and a dependent
variable, which can be used to predict future values of thedependent variable. In the context of stock market forecasting,multiple regression can identify key factors that influence stock
prices, such as economic indicators, financial data, companyspecific information, and market trends, and then predict withsome degree of statistical confidence the future movements of
the asset prices.
Exponential smoothing is a time series forecasting techniquethat uses a combination of smoothing and trend analysis topredict future values. This method is particularly useful for datathat display seasonality, as it can capture and predict intrinsic
seasonal patterns in the data. Ultimately, the choice between
multiple regression and exponential smoothing will depend
PAGE 36 IFTA.ORG

on the specific nature of the data being analyzed. If the datacontains multiple independent variables that may influence
stock prices, multiple regression is more appropriate. On theother hand, if data display seasonal patterns, exponential
smoothing may be more effective.
It is worth noting that predicting the stock market is an
inherently uncertain task, and no forecasting model canguarantee accurate predictions. Therefore, it is important
to approach any stock market forecasting with caution andalways consider a range of factors, including market trends,
economic indicators, and risk factors. Moreover, it is mandatory
to rigorously assess all the statistical hypotheses in order tounderstand the limitations and pitfalls of the selected modeland to correctly interpret the analysis results.
This work has presented a rigorous evaluation of multiple
regression analysis, presenting a detailed assessment of all thetasks that must be performed for an informed and reliable useof multiple regression to forecast the underlying trend in theasset price movements.

Appendix Linear Independence andMulticollinearity
In multiple regression analysis, linear dependence among
the explanatory variables and multicollinearity are related
concepts, but they are not exactly the same.
Linear dependence among the independent variables meansthat one or more of the variables can be expressed as a linear
combination of the other explanatory variables. This implies
that there is a perfect linear relationship among some of the
independent variables, which can lead to a lack of identifiabilityof the regression coefficients and other estimation problems.
On the other hand, multicollinearity refers to a situation
where there is a high degree of correlation among theindependent variables, but not necessarily perfect linear
dependence. In other words, multicollinearity means that theindependent variables are highly interrelated, and it may bedifficult to determine the individual effect of each independent
variable on the dependent variable.
In summary, while linear dependence among the explanatory
variables is a more extreme case of multicollinearity,
multicollinearity can still occur even when there is no perfectlinear relationship among the independent variables.

References[1] Malkiel, B. G. “A Random Walk Down Wall Street.” W. W. Norton &Company, Inc., NY, U.S., 1996.
[2] Kaufman, P. J. “Trading Systems and Methods.” 5th edition, John Wiley& Sons, Inc., Hoboken, NJ, U.S., 2013.
[3] Spiga, B. “Trend Investigation: Operare in Tendenza con le Regressioni
Lineari.” Trading Library, 2022.
[4] Lincoln, T. H. “Time Series Forecasting: ARMAX,” Technical Analysis of
Stocks & Commodities, 1991.
[5] Kleinbaum, D. G., Kupper, L. L., Nizam, A., and Rosenberg, E. S.
“Applied Regression Analysis and Other Multivariable Methods.”
Cengage Learning, Boston, MA, U.S., 2014.
[6] Greene, W. H. “Econometric Analysis.” 8th Edition, Pearson
Education, 2017.

IFTA JOURNAL

2024 EDITION[7] Wooldridge, J. M. “Introductory Econometrics: A Modern Approach.”
7th Edition, South-Western Cengage Learning, 2019.
[8] https://finance.yahoo.com/[9] https://fred.stlouisfed.org/[10]Ramsey, J. B. "Tests for Specification Errors in Classical Linear Least
Squares Regression Analysis," Journal of the Royal Statistical Society
Series, 1969.
[11] Breusch, T. S. “Testing for Autocorrelation in Dynamic Linear Models,"
Australian Economic Papers, 1978.
[12] Breusch, T. S. and Godfrey, L. G. “A review of recent work on testing
for autocorrelation in dynamic linear models,” Journal of the Royal
Statistical Society, 1981.
[13] White, H. A. “Heteroskedasticity-Consistent Covariance Matrix
Estimator and a Direct Test for Heteroskedasticity,” Econometrica,
1980.
[14] Breusch, T. S. and Pagan, A. R. “A simple test for heteroscedasticity andrandom coefficient variation,” Econometrica, 1979.
[15] Jarque, C. M. and Bera, A. K. “Efficient tests for normality,
homoscedasticity and serial independence of regression residuals,”
Economics Letters, 1980.
[16] Ruppert, D. “Statistics and Data Analysis for Financial Engineering.”
Springer, 2011.
[17] Hyndman, R. J. and Athanasopoulos, G. “Forecasting: principles andpractice.” 3rd Edition, OTexts, 2021.
[18]Winters, P. R. "Forecasting Sales by Exponentially Weighted Moving
Averages," Management Science, 1960.

IFTA.ORG PAGE 37

IFTA JOURNAL

2024 EDITION

Christoph T. Wildensee, Ph.D., MFTA

Minute-Generated Price Values for Time Series
Analysis

Nordstr. 7
Seelze-Letter, Niedersachsen
30926 Germany+49 511 4302128
christoph@wildensee.de

Introduction
Time series of monthly average temperature and precipitation trends at different locations, recorded over longer periods of time up
to decades, allow the generation of prediction values for these locations and also bundled for regions with respect to a realistic viewon a development of such basic information. The same applies to a large number of other climate-related influencing variables. This isalso possible because seasonal fluctuations for each individual variable can be extracted via the models and thus adjusted trends anddifference patterns can be derived (ML / AI). An expected value in each case is known. This results in a comprehensible model-based
forecast outside of sudden exception restrictions. In the short-term forecast of the weather, forecast models are also used, which
represent in detail influencing variables such as wind, precipitation amount and center of gravity, temperature and solar radiation. The
quality of these is very high for one day and decreases with increasingly forecast days. The same applies to stable large-scale weather
situations, which also have a high forecast quality for the first day, but do not drop as much in quality for the subsequent days as in thecase of uncertain weather situations described above. What they all have in common is that the permanent observation and recordingof influencing variables takes place at many observation points with pinpoint accuracy and that their significance for the forecast
phenomenon is well-known [cf. e.g. also Trömel (2004), p. 27Ff].
A stock price that is displayed minutes later does not primarily depend on the previously emerging stock price trend [see Litz (2019),
pp. 15, 19ff, also Schmelzer (2009), pp. 5ff, 10]. Rather, the previous price merely forms a flank or tendency of the new price, around which
it fluctuates with a percentage offset. The expectations of market participants determine developments and are in turn supplied by both
legitimate and illegitimate information about companies, individuals operating in the corporate environment, governmental / fiscal policy
frameworks and other opinion leaders. A mathematically unambiguous description of this speculation is thus already difficult due tovery many factors that cannot be operationalized. Otherwise, it could not be explained that a person like Elon Musk could set the price ofBitcoin as well as Twitter into considerable „oscillations“ only by short text statements. The sensitive reaction of market participants to afew hyped opinions and their market actions can certainly convulse the market [see e.g. Businessinsider (2022)].
But if we assume that the pattern of past performance is a significant factor in short-term prediction and that all other factors
are so far behind in their effect that a mathematical description of this one factor is sufficient to make a significant forecast, becausesuch models work extremely well for medium- and long-term trend analysis, we can use a time series of past short-term performance togenerate a prediction value. The target should be divided: First, a value for the next time in the context of the choice of the integrationinterval in the minute range. But second, also a model use that targets a time period and later prediction value with such as weekly ormonthly basis.

Auto-Regressive-Moving-Average (ARMA) & Co.
Functional Models such as “Auto-Regressive-Moving-Average” (ARMA), ARIMA (integrated), SARIMA (seasonal) and others areavailable for value prediction [see e.g. Litz (2019), p. 41ff]. Here, we will discuss the use of an ARMA model. Such and derived similar
models are also supported, for example, in the software systems R and Python with many parameter setting options. If someone
would like to integrate this into program code and use thereby another language without integration of existing libraries, it isnecessary to make a transfer into the language logic. A representation of the Auto Regressive Moving Average ARMA(p, q) is done via...

what means

where AR(p) is defined as...

PAGE 38 IFTA.ORG

IFTA JOURNAL

and MA(q) as...

and can be integrated accordingly. A description for anadequate procedure is presented e.g. in Haile / Olive (2022)
as well as Hyndman (2017) and (2018) for ARIMA. It is notnecessary at this point to go into detail about the formula,neither about the mathematical derivation, nor about applied
optimizations / procedures such as Box-Jenkins, Yule-Walker(cf. e.g. also Schmelzer (2009), p. 8ff), error analyses and others.
This is done in an outstanding way at the mentioned place.
However, this procedure is at least codable.
We integrate the available prices every three minutes (nearly
200 points per day). In the following a with priority setting
adapted example code is used:[...]// i = > Array index; increase i++ to count_ds (number of records
with new values)// Example calculation with fitting; YTF = function value// ArrayNumNV[] = Array with values every 3 minutes from ≈8:30-18:30 (CET)
AR[i]:=beta1 * ArrayNumNV[i-1] + beta2 * MA[i-1];
MA[i]:=ArrayNumNV[i] - AR[i];DY[i] :=ArrayNumNV[i] - ArrayNumNV[i-1];
TRY // Attempt to create value
YTF[i]:=ar1 + ArrayNumNV[i-1] +(c1 * (ArrayNumNV[i-1] - ArrayNumNV[i-2])) +(c2 * (ArrayNumNV[i-2] - ArrayNumNV[i-3])) +(c3 * (ArrayNumNV[i-3] - ArrayNumNV[i-4])) +(c4 * (ArrayNumNV[i-4] - ArrayNumNV[i-5])) +(c5 * (ArrayNumNV[i-5] - ArrayNumNV[i-6])) +(c6 * (ArrayNumNV[i-6] - ArrayNumNV[i-7])) (ma1 * (DY[i-1]));EXCEPT// in case of error the value remains as read out
YTF[i]:=ArrayNumNV[i];END; // End try

2024 EDITION

This procedure is interesting because the last values areused via the factors / parameters beta1, beta2 and c1-c6 anda relevance is assumed that cannot be denied, since the last
6-15 values reveal the short-term trend (up to 15, since the last
relevant value is used offset in the case of repeated values). Values
further back are largely irrelevant to the short-term analysis.
The factors can of course vary depending on, for example, themarket affiliations considered.
ETF[i]:=ArrayNumNV[i] - YTF[i];// Passing the target prediction value to the variable value_predvalue_pred:=YTF[count_ds];
However, corrections of the output value due to different
stock price levels are necessary, as the last movements of theprice development often determine the direction and have to
be included. Basically, it is also true that occasionally omitted
values are not detrimental if you do not want to use theprediction value again immediately. In that case, it is necessary
to wait for an interval.

Results
The underlying model (values supported by DLL) shows thatwithout using existing library-based integrations specificallydesigned for this purpose, mapping such a systematics is still
useful and possible, and that modeling it can lead to success. The
not questioned taking over of supplied functionalities meansthat if necessary adjustments and mental reinterpretations
do not (can) take place any longer. The represented approachof an own programming is arduous, but can offer interesting
possibilities. Thus the exemplary representation of the stock
development of MODERNA shows a small error rate between
determined and prognosticated value (few extreme value
outliers: max. 7.49 EUR, min. -2.61 EUR) and only rarely ahigher deviation between prognosticated value and next value
determination than +- 0.5% .

IFTA.ORG PAGE 39

IFTA JOURNAL

2024 EDITION

Figure 1: MODERNA, between 2023-01-17 and 2023-01-25 - value and variance trends.

The analysis of the basic data for this period then also makes it clear that the model reacts quickly to these in each case for all
stocks and adjusts the prediction to them, despite clearly recognizable trends and occasional outliers. Those outliers, both
downward and upward, of course cannot be predicted (not model-based determinable; see as a later example the loss of the stock
value of near -60% of TUI between 2023-02-24 and 2023-03-31), but they can nevertheless be identified and displayed. In this way,
they are immediately in focus for the user and can be placed in context.
Figure 2: Between 2023-01-17 and 2023-01-25 and between 2022-10-14 and 2022-12-23 (DAX had reached the level of
13940 points on 2022-12-23) - Percentage distribution of difference outliers across all stocks.

(< -1% includes values of < -2%; > 1% includes values of > 2%)

PAGE 40 IFTA.ORG

IFTA JOURNAL

2024 EDITION

Other short-term Interval views
Determining a prediction value for a point in time further in the future - for instance a week or a month here - is more difficult.
This view is not dependent on the last value, but must first be seen on a larger scale. As a weekly view, the base is about 1000 points
back from the last determined value, in the monthly view about 4000 points away. So, if someone analyzes these two views with theidentical systematics like in the minute-range, constantly going back in e.g. 200 resp. 800 points (1000 resp. 4000 points by 5 daysa week = 200 resp. 800 points per step), a stable view on the next period can be determined. For this purpose, the respective interval
has to be identified, which is included in the partial view. This means a change of the definition of the relevant evaluation vectors, sothat [i-1] to [i-7] is substituted by the - starting from the last point and going back per 200 resp. 800 points per step as a vector - thenavailable reference points for the use in the determination formula. It is therefore pretended that only these values on average of the
sub-ranges and not the large number of intermediate values have been surveyed.
Seasonal corrections are inappropriate, as there are slight price movements around the time of the dividend payment and at a few
other points, but these are not generally significant over the period and these interval views.
Figure 3: Short-term differences 1W/1M between 2023-02-03 and 2023-03-03 respectively 2023-04-03.

The result is (provided that the price values are collectedconsistently every weekday during the trading period) a shortterm forecast on a weekly and monthly basis, which can beassessed as model-based, comprehensible and reproducible.
(Documentation via F5 Show Hist. - Button „1W/1M“ with files
in the application directory.) However, as the time horizon
increases, the validity of these prediction values decreases
and they may not be adequately reflected in the case of large
fluctuations. Figure 3 shows that a forecast for one week
and one month does not approximate actual performance.
However, if there is also such a setback as in the 6th calendar
week 2023 (Feb., 10th), this stronger deviation is to be expected.
A better and impressive example is the development in the
11th and 12th calendar week with the changes in the ECB's key
interest rates by +0.5%, the bankruptcy of Silicon Valley Bankand other banking difficulties, and the upheavals in the Swissbanks Credit Suisse with UBS as the stronger player (emergency
rescue deal; stemming financial market panic). Every stock
trended downward. These days diverse factors impacted stock
performance significantly.

Figure 4: Between 2023-02-02 and 2023-04-06 - Percentage
distribution of difference outliers across all stocks - Result
during downward trend.

IFTA.ORG PAGE 41

IFTA JOURNAL

2024 EDITION

Finally, it can be seen that the model can react very quickly to changes in the minute range as shown, however, it can be understoodthat an appropriate reaction to sudden changes in the market cannot lead to an adjustment of a prediction value in the weekly andmonthly range, since these changes take without temporal reference to the model. Then the model can no longer make corrections
to the predicted value in a timely manner and becomes uncertain in its consideration of market influence. The consequence is a
detachment of the prediction value from a realistic view of the market development due to the various messages from the market
players.

Parameter profile
Each choice of parameters in a range between -1 and 1 with step 0.01 leads to an individual profile curve in a simulation, whichshows how close the deviations between prediction and actual value are (Figure 5; x = number of values [c], min. 1000; y = abs.
deviation in EUR; z = model response per chosen parameter setting between -1 and 1 with step 0.01). These profiles are therefore
important for the choice of model parameters. If the curve for one or more particular parameters runs towards 0 for all values, while
the other parameter variants show outliers up or down, this chosen parameter is eligible. Frequent strong outliers per subcurve are
an indication that the model reacts too slowly with this parameter setting. This must be checked for all parameters and applied inparameter context.
Figure 5: Example of a Parameter Profil - Continental, c5, -1 (left) to 1 (right) step 0.01.

Conclusion
Even if it is mathematically ambitious at first to use sucha model adjustment for near-minute forecasts when pricevalues are collected in a minute-range, the procedure offersa valid result. ARMA / ARIMA models and similar ones are justestablished as linear, time-discrete models for usually shortterm economic forecasts. The fast adjustment is immediately
included in the next calculations even in case of strong ad-hoc
fluctuations and it shows a considerable performance for thisportfolio.
The vector-adjusted but identical model usage for othershort-term intervals (week, month) is more difficult, as it shows
weaknesses especially when strong ad-hoc swings occur, but
the low sensitivity for such ad-hoc events is also the goal. For
this reason, a weekly view is also rather unsuitable for themodel presented here with its parameters. This is too close to
get a good approximation when short-term oscillations occur.
In this respect, it also shows that a model with parameters forthe near-minute forecast is not appropriate for other short
PAGE 42 IFTA.ORG

periods. They require different model parameter settings. The
last period in each case needs a higher priority in the model togenerate valid values. Thus, strong upward or downward trends
are observed with a considerable delay. More market data isrequired and must be analysed and conditioned.
As a result, however, the model can be used to justify further
variant analyses for test purposes.
FIBO_VIEW.ZIP provides an application that can be used
to observe and experiment with the model over an extended
period of time. If you want to get the source code and / or an
actual database, send me an email (DLL start must be possible).
(Group of stocks: Adidas, Nel ASA, Drägerwerk, DWS,
Moderna, Biontech, Siemens Energy, Continental)

References
Businessinsider (2022): What happens when Elon Musk moves markets
with a tweet, Date 2022/05/31, https://www.businessinsider.com/
what-happens-when-elon-musk-moves-markets-with-tweet-2022-5.

IFTA JOURNAL

Chan / Chen (2011): Subset ARMA selection via the adaptive LASSO,
Statistics and its Interface 4, 197-205.
Eshel (2003): The Yule Walker Equations for the AR Coefficients,
University of Pennsylvania.
Haile / Olive (2022): Forecast Intervals for Some ARIMA Time Series,
Southern Illinois University, September 20, 2022.
Hyndman (2018): Forecasting: principles and practice, 2 ARIMA models,Monash University Business School, https://robjhyndman.com/
acemsforecasting2018/2-ARIMA.pdf .
Hyndman (2017): Forecasting: principles and practice, 2.4 Non-seasonal
ARIMA models, Monash University Business School, https://
robjhyndman.com/uwa2017/2-4-NonseasonalARIMA.pdf .
Litz (2019): Vorhersage von Aktienkursen mithilfe rekurrenter
Neuronaler Netze, Masterarbeit, Hochschule Harz.
Schmelzer (2009): Die Volatilität von Finanzmarktdaten - Theoretische
Grundlagen und empirische Analysen von stündlichen
Renditezeitreihen und Risikomaßen, Diss., Universität zu Köln,
2009.
Stadnik et. al. (2016): Fourier Analysis for Stock Price Forecasting:Assumption and Evidence, Journal of Business Economics andManagement, 2016 Volume 17(3): 365–380.
Tang / Röllin (2021): Model identication for ARMA time series throughconvolutional neural networks, Decision Support Systems, Volume
146, 2021.
Trömel (2004): Statistische Modellierung von Klimazeitreihen, Diss.,
Universität Frankfurt am Main, 2004.
Wildensee (2022): http://www.wildensee.de/fibo_view.zip . http://
www.wildensee.de/laz1a.htm .
Wildensee (2023): Raw Values, http://www.wildensee.de/raw_val.ods .

2024 EDITION

Christoph T. Wildensee, Ph.D., MFTA, is a Senior Auditor of ITRisks and a Data / Process Analyst from Germany. He takes careof accounting-related IT-Systems such as SAP, but also Trading
Systems.

IFTA.ORG PAGE 43

IFTA JOURNAL

2024 EDITION

Michael Trequattrini, CSTA

Validation of a Trading System: Monte Carlo
Analysis Applied to the IS & OOS Architecture

Terni (TR), 05100, Italy+39 3470010554
michael.trequattrini@gmail.com

Abstract
This article aims to present a model for analyzing the robustness of a trading strategy, which, applied ex-post to the development
and validation chain, will allow the determination of the probability of robustness on future and unknown data. In its various
declinations, the model will be applied to a real and already validated strategy, focusing on interpreting the results achieved.

Choice of the Validation Architecture
A crucial step in the development of a trading strategy is the identification of the correct validation architecture. This, in its staticand dynamic versions, allows the trader to segment the entire historical series available by obtaining an "In Sample" and an "Out of
Sample" period. Regarding the static declination, which originates from Machine Learning, Figure 1 highlights several architectures
found in the literature today. Without delving into each of them in detail, which would be beyond the article's focus, it is emphasizedthat the model presented can be applied to any architecture, making a choice fall based on personal needs and ways of working.
Figure 1: Validation architectures

In this article, for the application of the model, will be used a trading strategy coded according to the architecture “E”, called GSA(“Gandalf Segmented Architecture”) and first presented at the IFTA 2017 event by the R&D group Gandalf Project. This approachmakes it possible to eliminate the incubation period and to model and test the system under all trend and volatility conditions. It will
also provide a robustness indicator, called GPDR, which will return an objective measure of persistence by comparing the swarmof the trades of the Is Sample and Out of Sample periods. Any value greater than 1.0 will indicate the robustness of the results andsubsequent success in the validation process. It can learn more about the GSA architecture and the GPDR indicator in an article in the
SIAT Mag #07.

Origin of the Model
The trading strategy to which the model will be applied is a breakout system on the hourly series of the Gold Future. Without
analyzing the system's rules, suffice it to say that it has been adequately validated with a GSA in light of a GPDR of 4.5. Figure 2
shows the validation architecture: in yellow, the In Sample training periods, in light green, the Out of Sample testing periods, andfinally, in darker green, the equity line of the system superimposed on the Gold Future. The size of each IS, and OOS block is equal to2300 candles giving rise to a symmetric architecture. This choice is arbitrary and could result from discretionary logic or random
assignment. In either case, the choice will affect the entire development chain. Think of optimizing the parameters of a strategy;
inevitably, the results will depend on the segmentation chosen. Different splitting of the time series implies performing the
optimization, at least in part, on different data and consequently will produce results with some degree of dissimilarity. If the varianceof the results produced by the optimization, when varying IS and OOS segmentation, is reduced to the limit with the GSA technique,the same cannot be said for the other architectures. Moreover, whether GPDR or any other analysis is used, the validation process canlead to different results as the fractionation varies. Therefore, the event to be averted is when a system passes the validation due to a
PAGE 44 IFTA.ORG

IFTA JOURNAL

good choice of IS and OOS split. Obviously, during the strategy
development, the trader should choose and rely on a specificsegmentation. For this reason, the model is only applied ex-post
to the trading system's development and validation chain.
Its goal is to test whether the strategy passes the validation
process even with different segmentations of the training andtesting blocks.
Figure 2: Trading system on Gold Future with a GSA

2024 EDITION

Model Operation
The first step is creating several N validation architectureswith different random segmentations following a Monte Carlologic. For each of them, the backtest is performed on both the
In Sample and Out of Sample portions. The key metrics arecomputed, and the validation test is performed (in the personalcase using the GPDR indicator). At this point, it is counted
how many times, out of the total N, the system passed thevalidation. If we are beyond a certain percentage of validated
tests, that percentage can be seen as the probability of futuresystem robustness. Figure 3 shows the model inputs, a thoroughunderstanding of which is required for consistent results.

Figure 3: Model inputs

Since the strategy on Gold Future was developed with symmetric GSA, the new architectures must adhere to that pattern. It will
suffice to change the specific parameter to obtain random segmentations with the IS portion greater than the OOS one. It is asked togenerate 1000 GSA architectures with different segmentations, a minimum number of blocks equal to 8 (4 IS + 4 OOS), and a minimum
unit block size of 3% of the whole time series. The GPDR validation threshold is set at 1.0, and the tolerance at 10%. Two of the thousand
random architectures generated can be seen in Figures 4 and 5. Note how in the first case, the size of each block is 4208 candles, whilein the second of 9213 candles. It can be easily seen how the validation in these two situations could lead to different results.

IFTA.ORG PAGE 45

IFTA JOURNAL

2024 EDITION

Figure 4: Random generation #1

Figure 5: Random generation #2

Figure 6: Results

Finally, a comparative analysis of the primary metrics
produced by the backtest is shown in Figure 7. The mean andstandard deviation on the IS and OOS aggregates of all 1000
generated architectures are calculated for each metric. A delta
between +-30% ensures acceptable variation.
Figure 7: Comparative analysis

Results Interpretation
Once the 1000 random architectures have been generated,
it is time to evaluate the results. Figure 6 shows the model's
output, which provides several indications for an overall
assessment of the robustness of the strategy. The key element,
the subject of the entire article, is the "Probability of futurerobustness," which, in this specific case, shows that thetrading system passed the validation process 73.4% of thetime. As per its name, this same percentage can also be readas the probability of robustness on future, unknown data.
Remembering that the model is applied ex-post to a strategy
that has already been validated with an initial segmentation,
it is sufficient to have a value greater than 50% (if desired, thethreshold can be raised, making the model more selective). With
the GPDR distribution available, additional information can beobtained by decomposing it into deciles. As in the present case,
it is pleasant to find a value greater than 1.0 from the median orprevious deciles.

PAGE 46 IFTA.ORG

Noise Addition
As mentioned earlier, the result of the optimizations in thedeveloping phase is conditioned by the initial In Sample and Out
of Sample segmentation. The possibility of applying random
noise to the strategy parameters was introduced to accountfor this within the model. In this way, since each segmentation
would have led to a diverse optimization, the analysis is moreconsistent, simulating the likely difference in results. Figure
8 shows the final input panel, with the amount of noise to be
applied.

IFTA JOURNAL

2024 EDITION

Figure 8: Model inputs

Figure 9 shows the model's output using the same 1000
segmentations generated earlier with the addition of a 20%
random noise added to each strategy parameter. Note how
adding different noise to each newly generated segmentation
results in a lower validation rate than obtained without noise.
It should be noted that no result is more frequent than another,as it depends on how one chooses the parameters during
optimization. As an indication, running the model with andwithout noise is advisable, holding constant the segmentations
generated at the first run (using a specific random seed)and verifying that the "Probability of future robustness" issufficiently high in both cases.

Figure 10: Noisy equity lines

Figure 9: Results with noise

Conclusion

Finally, Figure 10 depicts the swarm of equity lines produced
by noise addition. The desirable situation is the one with theoriginal equity line located approximately in the middle ofthe cloud, highlighting a proper optimization process at thedeveloping stage.

The model presented here allows an additional checkon the robustness of a strategy already validated with an
initial architecture. The possibility of testing the system on
different segmentations makes it possible to identify thosesituations where the validation has been passed due to the
choice, voluntary or not, of a specific IS and OOS fractionation.
Furthermore, it is fair to point out that although the model
proposed here sees only the declination with or without noise,
it is possible to imagine many variations on the theme. The goal
was to share an idea of analysis that can be customized to help
traders evaluate the robustness of a trading system.

IFTA.ORG PAGE 47

IFTA JOURNAL

2024 EDITION

The Impact of Machine Learning and Computer
Vision to Predict an Opening Range Breakout on
E-Mini S&P 500
Abstract
The motivation for using artificial intelligence to create
accurate models for trade optimization and price prediction isincreasing and nowadays potentially usable for every trader.
Depending on the instrument, the trading hours, and thetimeframe, different combinations of technical, financial,macro-economic, and sentiment indicators can be either more
effective or less suitable. There is no general consensus about
the ideal mix of indicators that are most relevant for predicting
price movements. To keep their work simple and clear, traders
should focus only on a few. Machine learning is a powerfultool to help traders adapt their indicator setup to the market
and improve their strategy. The use of neural networks totrade suitable indicator combinations for specific markets andtimeframes has as yet been relatively underexplored. Basedon machine learning and “computer vision” approaches, weinvestigated 19 indicators to identify the optimal combinationof indicators for predicting a significant price movement after
the opening range of the E-Mini S&P 500 Futures. We also
implemented two self-programmed indicators: the intra-bar
price movement (IBPM) indicator based on computer vision, andthe high-frequency presence (HFP) indicator based on shortterm cycle analysis (STCA) using fast Fourier transformation on
price and volume data during the opening range. Both indicators
are very useful for predicting a significant trending pricemovement after the opening range period. We argue here thatthe strategic choice of an indicator combination by an optimized
neural network can predict a short-term trend with an accuracyof about 80% during specific market conditions.

Acknowledgements
I could not have embarked on this journey without thestaff of the VTAD – the Vereinigung Technischer Analysten
Deutschland (the German Association of Technical Analysts) –who generously offered me their knowledge and expertise.
I would also be remiss in not mentioning my wonderful wife
Berenike and children Marika, Lara, Marius, and Laurenz. Their
belief in me has kept my spirits up and motivation high during
this process.

Introduction
1.1 The Opening Range
The “opening range” refers to a specific time period atthe beginning of a trading session during which the pricerange of a security is established. It is characterized by ahigh price volatility and momentum. Opening range can be
defined in a time-based way from a few minutes up to two
PAGE 48 IFTA.ORG

Edzard Wiener, Ph.D, MFTA, CFTe
Vereinigung Technischer Analysten
Deutschlands e.V.
Berlin, Germany
edzard.wiener@gmail.com

hours, or as pattern-based, in terms of movement up until thefirst significant price reaction, such as an intra-day microtrend, a broad or tight channel or a swing. The pattern-based
characterization implies a flexible definition that varies eachday. The opening range is determined by the highest and lowest
prices at which a particular security trades. Traders should pay
close attention to the opening range because these can provide
valuable information about market sentiment and potential
trading opportunities.
The first 30 minutes following the opening of the market
is a particularly intense period, as buyers and sellers look
for advantageous positions. During this time, incoming
orders can lead to considerable price volatility. Such dynamic
pricing behavior is often triggered by institutional traders
who typically participate in the market with high-volumetransactions. Some traders will even wait longer – such as awhole hour – to gauge the balance of power between buyers
and sellers. They than develop a trade plan in the direction of a
possible breakout.
The idea of analyzing the start of a trading session to gain
information about possible price movements during the session
was first established by J. Peter Steidlmayer, a trader at the
Chicago Board of Trade (CBOT). He developed the concept known
as “initial balance” as part of his Market Profile theory in the
1980s, especially in relation to futures trading (Steidlmayer2002). Based on his observations he noticed that the initialbalance can provide important insights into the market’s
behavior for the rest of the trading day. For example, if theinitial balance is skewed to the upside, it might indicate bullish
sentiment, while a downside skew might hint at a more bearish
sentiment. The high and low of the initial balance can act as
support and resistance levels for the rest of the trading day. The
size of the initial balance can indicate the potential volatilityof the market for the day and if the price moves significantly
outside the initial balance range, this could indicate a potential
breakout.
Nowadays the definition of the initial balance is interpreted
more flexibly. With the recent rapid advances in technology andthe growing influence of artificial intelligence, we would like totake a closer look at this specific time period at the beginningof a trading session and analyze it again using a combination ofnewer indicators and the power of machine learning to optimize
trading on a shorter timeframe after initial balance. Motivatedby Steidlmayer’s approach, the following question arises: is it
possible to predict a significant price movement after the initialbalance through a suitable selection of indicators and the use of
artificial intelligence?

IFTA JOURNAL

In this study we focused our attention on the very liquid
future market, in particular the E-Mini S&P 500 Futures. We
used the NYSE opening time of 9:30 a.m., when the market
opens and a high volume of trading is coming in. For an intraday trade it is best to wait for the market to stabilize, thendetermine the trend and try to look for an entry. Opening range
breakout patterns can help to find some of the strongest chartsfor day and swing trading (Calhoun 2015, p 20). In this context
we used a time-based definition of the opening range as the first
30 minutes of each trading day, in order to look for successful
breakouts and a consequent trending price.
1.2 Technical Indicators
Technical indicators are mathematical formulas used to
identify patterns and trends in the market. Frequently they
are lagging indicators, but they can help to generate insights
into future price movements. Since markets are by theirnature never perfectly efficient due to various factors such as
information asymmetry, investor irrationality, and transaction
costs (Shiller 2003, p 83, Malkiel 1998, p 59), technical analysis
and indicators are crucial tools and commonly used, especiallyfor short-term trading strategies. There are many indicators
used in technical analysis, such as trend indicators, oscillators,
volatility indicators, volume indicators, market breadth,and sentiment indicators (Fang 2014, p 25). Indicators are
increasingly being combined over a wide range of timeframes,
while a host of instruments and newer approaches are now
finding their way into trading, such as social media-based
sentiment or time series analysis (TSA), as well as tools for
identifying seasonal trends (or seasonality) and shorter-term
cyclical patterns (Warren 1984, p 123). Innovative approaches
like algorithmic trading based on AI are also increasingly
being used by retail traders and can offer several advantages,
regardless of the particular trading style preferred.
1.3 Machine Learning – Neural Networks
Neural networks are a subset of machine learningalgorithms ostensibly modeled on the workings of the humanbrain. They have been trained to recognize patterns andinterpret data by simulating human cognitive operations(Kumbure 2022, p 21). In the world of trading, neural networks
are powerful tools that can be used to predict prices, recognize
patterns or optimize portfolios. Building a neural network
requires several steps. First, a clear hypothesis needs to bedevised and addressed. Then data must be collected andprepared for modeling. This procedure includes data cleaning,
primary statistical analyses, normalizing and data splitting intofeature and response variables, and subsequently into a training
and testing data set. The architecture of the neural network
then needs to be designed, based on the hypothesis and theamount and structuring of the data. So-called hyperparameters,such as the number of layers, the number of nodes in eachlayer, and the activation function also have to be optimized.

2024 EDITION

For the most effective selecting of hyperparameters, theneural network has to be trained and the setup with the lowest
validation error should be picked.
During the training phase, in this study the network’s
predictions were compared to the actual values and the weights
and biases adjusted to minimize the difference between
predicted and actual values. As this procedure is itself based on
the performance of the network, it thus represents an iterative
process of optimization. This step requires large amounts ofdata which are often difficult and expensive to obtain. After
this initial training phase, the network is then validated usinga smaller test data set. Once the network is up and running,
predictions can be made on newer – and as yet unseen – data.
1.4 Computer Vision Algorithm
Computer vision is a method that uses artificial intelligence(AI) to acquire and analyze digital images to extract richly
descriptive – or high-dimensional – data from the real world
to produce quantifiable, numerical information. The approach
attempts to replicate the complexity of human experience (or“vision”) with the aim of using its processing of the featuresof digital images in order to automate tasks that our visualsystems typically carry out. In the field of trading, pricemovements and pattern recognition in real time could be a
promising application of this technology. Price movements oneach trading platform can be observed and stored like frames
from a film. The images are than post-processed to enhance
the feature of interest, which can involve resizing the images,
converting them to different colors or applying filters. In a next
step, structure detection, using segmentation, edge detection ormore advanced techniques like convolutional neural networks(CNNs) can also be deployed. Characteristic patterns and typicalsetups can be extracted and converted into a numerical format.
For example, intra-bar price movement (IBPM), defined as theprice changes during the formation of a graphically represented
candle can be detected and the current rate (or velocity) of pricechange as well as the current deviation from the opening pricecan be extracted for further real-time analysis. This process canbe complex and may require advanced techniques depending on
the quality and complexity of the images (Chen 2016).

IFTA.ORG PAGE 49

IFTA JOURNAL

2024 EDITION

Table 1 Technical indicators as feature variables for the neural network

Indicator group
Indicators based on COT
sentiment(weekly Commitments ofTraders report)

Indicators based on bars

Indicators
COT position change:

Description

net long [1] or net short [-1Shows the net long and short positions of commercials andnon-commercials. Changes in these positions can indicate
shifts in market sentiment

COT percentage change in relation toprevious week

Shows the percentage change in COT positions in relation to
the previous week.

30-minute bar of opening range:

Compares the closing to the opening price of the 30-minuteopening range bar:bullish or bearishbullish (green bar) or bearish (red bar)
Bar size of 30-minute opening rangebar:Categorizes the size of the 30-minute opening range bar:large body or small bodylarge or small
Wick size of 30-minute opening rangebar:Categorizes the size of the wick of the 30-minute opening
range bar:large or smalllarge wick or small wick

Ratio of bullish to bearish bars on oneminute opening rang

Compares the number of one-minute bullish to one-minutebearish bars during opening range.

Location of 30-minute opening range
bar:

Indicates whether the 30-minute opening range bar is inside or
crossing the previous day’s trading range (TR).

inside [0], crossing above [1] or crossing
below [-1] theprevious day’s high or low
Indicators based onvolumeVolume profile shape over opening
range:

Indicates the shape of the volume profile over the opening
range, which can suggest different market conditions.

D-shape, I-shape, b-shape, P-shape,
double distribution,
non-significant shape
Point of control (POC):
above [1] or below [0]Compare the location of the30-minute opening range bar in
relation to the weekly point of control. The POC is the pricelevel with the most trading activity.

Volume during opening range in relation Indicates the trading vol-ume during the opening range into a 14-period “lookback” timeframe:
relation to the av-erage volume calculated as the moving
average from a 14-period “lookback” timeframe.
over, normal, under average volume
Indicators based on VWAP
(volume weighted average
price)

30-minute bar of opening range in
relation to the VWAP line:
above [1] or below [-1] VWAP

PAGE 50 IFTA.ORG

Compares the location of the 30-minute opening range bar in
relation to the VWAP line.

IFTA JOURNAL

2024 EDITION

30-minute bar of opening range in
relation to the VWAP band:
above [1], below [-1] or inside [0] the firststandard deviation VWAP band

Compares the location of the 30-minute opening range bar to
the first standard deviation VWAP band.

Indicators based on
seasonality

Weekday of opening range[Monday to Friday]

Takes into account the weekday of the opening range based on
the assumption of a variety of trading activities.

Indicators based on highfrequency presence (HFP)
using fast Fouriertransformation on shortterm cycles

Presence of high frequency in pricedata:

Indicates the presence of high frequencies in the price data
during the opening range, indicating strong trading activity.

Spectrogram of price[time vs. frequency vs. intensity]
Presence of high frequency in volume
data:

Indicates the presence of high frequencies in the volume data
during the opening range, indicating strong trading activity.

Spectrogram of volume[time vs. frequency vs. intensity]
Indicators based on
intra-bar price movement(IBPM)
using computer vision

Moving average indicators

Number of high-velocity pricemovements
during formation of a 30-minute bar

Uses computer vision techniques to track the movement of theprice line on the chart and to identify impulsive, high-velocity
movements.

Standard deviation of price movements
in relation to the opening price of a30minute bar

Uses computer vision techniques to measure the standard
deviation of the actual price line in relation to the opening
price of that bar.

Price in relation to the EMA 20 line:

Compares the price to a 20-period exponential moving average(EMA). Prices above the EMA are often seen as bullish, while
prices below the EMA are seen as bearish.

above [1] or below [-1]Materials and Methods
2.1 Input and Response Variables
The feature variables incorporated into the neural network spanned various types of financial indicator (Table 1) and were plotted on
the price or volume chart. For the sake of simplicity, the variables are based either on mathematical calculation and documented as metricvariables or visually evaluated on the charts and categorized according to the number of possible values – 1, 0, -1, large or small – mostly in
relation to a mean value or to previous values.

IFTA.ORG PAGE 51

IFTA JOURNAL

2024 EDITION

Figure 1 Candlesticks Charts from the E-Mini S&P 500 with technical indicators – opening range market movementsof the E-Mini S&P 500 Future during the first half-hour of a typical day’s trading; Figure 1(a) - (c) shows consecutive
bullish candles (in light blue or green), also anticipated by the neural network.

The technical indicators were applied on a 30-minuteand one-minute chart (Figure 1). The data were analyzed ona NinjaTrader platform (version 8, NinjaTrader Group, LLC)
including third party add-ons for flexible volume profile (Trader
Dale). All data were entered into an Excel spreadsheet for
further evaluation. The whole data set consisted of 1260 datacells (21 indicators x 60 days) including a training, testing, and(for prediction) an unseen data set.
The data feed for the futures markets during regular
trading hours was obtained by means of Kinetick data feed
(Kinetick market data). The following price values were
downloaded: open, high, low, close (often shortened to OHLC),and volume, on a “tick” basis of the E-Mini S&P 500 3-2023 andE-Mini S&P 500 9-2023 future contracts covering the period
from January 1 until March 31 (for training and validation), andfrom the E-Mini S&P 500 September contract from July 1 until
July 14 (for prediction). Finally, 19 indicators were used to obtain
the input data for the neural network.
Short-term seasonality was considered by documenting the
weekday of the daily opening range to consider the impact ofrecurring price patterns that occur during specific times of theday.
Market sentiment was analyzed using the weekly
Commitment of Traders report (COT) data released by the U.S.
Commodity Futures Trading Commission (CFTC). The reportoutlines the number of futures contracts held by market
participants (hedge funds, banks, producers, and speculators,
for example). Two main categories have to be distinguished:
PAGE 52 IFTA.ORG

commercial market participants deal in the futures market forhedging, and their positions are negatively correlated with theunderlying market; and non-commercials, which deal in the
future markets for speculative reasons, and whose positions
are positively correlated with the underlying market. To
indicate shifts in market sentiment, the net positions and theabsolute weekly percentage position change of commercials andnon-commercials were calculated and entered into the Excel
spreadsheet. The net positions were categorized as -1 for a shortposition and +1 for a long position.
The trading volume and mean volume over a 14-period
lookback period was calculated and plotted below the pricechart (Figure 1). The actual trading volume was categorized inrelation to the mean value. If actual trading volume was below
average, it was categorized as -1. If actual trading volume wasnear the mean value, it was categorized as 0 and, if the trading
volume was above the mean volume, this was categorized as 1.
The number of bullish and bearish candles was counted
during the opening range on a one-minute timeframe and thegreen (bullish) to red (bearish) candle ratio was calculated anddocumented. This strategy is known as bar counting (Brooks,
2011).
The relationship between candle body size to wick size wasassessed on a 30-minute timeframe and visually categorized aslarge, equal or small.
As a short-term trend indicator, the exponential moving
average with a 20-period lookback period (EMA 20) was used
to identify short-term trends. Based on visual inspection of theIFTA JOURNAL

opening range, the price in relation to the indicator line was
documented. If the price was mostly being traded above EMA 20
it was encoded as 1 or, if below, it was entered as -1.
The weekly volume profile and its point of control (POC)
indicating the most traded price over this time period wasplotted on the one- and 30-minute charts. The traded price inrelation to the weekly POC was evaluated. A price above the POC
line was categorized as 1 and below as -1.
In addition, a flexible volume profile over the daily opening
range was plotted on the one-minute chart and the shape of thevolume profile was analyzed visually and classified as either a
D-shape, I-shape, b-shape, P-shape, double distribution (DD) or
a non-significant shape (non). The shape of the opening range
volume profile is useful for gaining market insights and allows
a more nuanced grasp of market dynamics, auction processes,
and price action, which can all influence the patterns of further
daily trading.
The daily volume-weighted average price (VWAP) is
calculated by multiplying the price of each trade by the numberof shares, then summing these values and dividing the result
by the total volume. This is a key benchmark for traders,
especially for professional traders whose aim is to buy below
and sell above. Deviations of the price from VWAP may indicate
overbought or oversold conditions. If the price is trading above
VWAP the indicator line is represented in green and categorized
as 1, and if the price is trading below VWAP it is represented in
red and categorized as -1.
Furthermore, the trading price was evaluated in relation
to the first standard deviation band of VWAP. If the price
was trading above the first standard deviation band, it was
documented as 1. If the price was trading below the firststandard deviation band, it was documented as -1, and in
between as 0.

2024 EDITION

The previous-day high (green dashed line) and previous-day
low (red dashed line) were also plotted on the one-minute and30-minute chart. If the actual price was above the previousday high it was notated as 1. If the actual price was below theprevious-day low, it was entered as -1 and, if it was in between,
this was recorded as 0.
2.2 New Indicators: Intra-Bar Price Movement,
High-Frequency Presence
In addition, two proprietary indicators were applied for thisstudy: the intra-bar price movement (IBPM) indicator, deploying
computer vision (CV) techniques, and the high-frequency
presence (HFP) indicator conducting short-term cycles analysis(STCA) of price and volume data during the opening range. The
analysis was carried out within one short timeframe comprisinga one-minute chart.
The IBPM indicator is based on computer vision andcalculates the speed of price change during candle formation.
Therefore, the movement of the price line was recorded inreal time from a candlestick chart and refers to the pricefluctuations that occur during the predefined period. A pricecandle represents a specific time period during which the priceof a financial instrument may undergo various price movementswith different speeds and deviations from the opening price ofthat candle. The IBPM indicator measures the position of thecurrent trading price relative to the open price. The IBPM could
be useful evidence because it provides traders with insights into
the conditions underlying very short-term price dynamics andvolatility.
The presence of high-speed price movements, defined as avalue greater than 250, can be interpreted as an indication ofstrong trading activity. This suggests the presence of market
participants who have the ability to move the price rapidly in aparticular direction.

Figure 2 IBPM indicator on price and volume data over opening range (60-minute bar on July 7, 2023)

IFTA.ORG PAGE 53

IFTA JOURNAL

2024 EDITION

Figure 2(a) depicts a bearish small body candle (red)with a large lower wick. The IBPM indicator identifies thestrong trading activity between buyers and seller during theformation of this candle (Figure 2(b-d)). Multiple strong pricevelocity changes of more than 250 in both directions withlarge deviations from the opening price (Figure 2(e-f)) can beobserved, indicating that buyers try to push the price closer tothe opening while the sellers try to stay in control. Figure 2(g)clearly demonstrates that the most frequent location during
the candle formation is the opening price corresponding to thezero line. During the strong up and down movements, the zeroline is crossed several times until the “closing” of this candle.
The candle in this example is a kind of reversed candle with asmall body and a large lower wick following three green bullish
candles, each with higher closings. This pattern after a reversal
or a period of consolidation is also known as the “three whitesoldiers” and is typically interpreted as a strong bullish signal,
indicating that buyers have taken control of the market.
Figure 3 High-frequency presence (HPF) exhibited inspectrograms representing either price (a) or volume (b)data

The basic concept of STCA is to determine whether it is best
to perform a trend or a swing trade. STCA over the opening
range using fast Fourier transformation (FFT) allows traders
to identify the underlying short-term periodicities and cyclicalpatterns present in price and volume data (Figure 3). FFT
reflects the duality between events in the time domain andtheir representation in the frequency domain. By analyzing
the dominant frequencies, traders can identify short-term
patterns in the market data. A trader might choose to entera long position when the dominant frequency suggests anupcoming bullish cycle. By examining the peaks and troughsin the spectrum, traders can determine the frequencies atwhich the market shows strong activities. For a detailed
evaluation, spectrograms of price and volume data were
calculated and plotted with time on the horizontal axis,
frequency on the vertical axis, and various colors from blue toyellow representing an increasing amplitude or energy of thefrequencies.
Figure 3 shows HFP as it appears in the spectrograms,
which represent either price data (Figure 3(a)) or volume data
(Figure 3(b)) over the opening range. In this spectrogram, theyellow color signifies the presence of high frequencies in thedata. This can be interpreted as an increased trading activity,
leading to significant price action. During minute 13 to minute21, high-frequency volume changes are present in the data and,after a slight lag, price action follows during minute 18 to minute
30. This is observable because of the growing number of yellow
areas during this time interval.
These indicators serve as input variables – in this caseknown as feature variables or predictors – and can help theneural network to learn specific patterns to provide valuable
information about the financial markets. All indicators haveshown predictive value in a similar context. Importantly,
while developing the neural network one has to consider
multicollinearity, among other indicators.
2.3 Model Training
Initially, the issue under study was whether it would bepossible to predict a significant price movement after the startof the regular trading session for a highly liquid futures contract
using various technical indicators. All numerical and categorical
data, obtained from the technical analysis of both a one-minuteand a 30-minute candlestick chart, were documented in an Excel
spreadsheet. All data were historical “tick data” – that is, all
non-aggregated intra-day prices of a security determined duringa trading day – from the March and September 2023 contractsof the E-Mini S&P 500. Overall, 60 opening ranges were analyzed
using 19 distinct indicators, as set out in Table 1 above. The
data set was then separated into a training and testing subset.
The neural network (NN) was created using MATLAB Version
R2022b, by MathWorks (McCarthy 2018).
The selection of a neural network’s architecture is often
discretionary and it is not always obvious why it has been
designed in that way. In total, 70% of the data are used fortraining, 10% for validation and 20% for testing. The processof training and validating the neural network constitutes aniterative optimization exercise with varying configurations of

PAGE 54 IFTA.ORG

IFTA JOURNAL

hyperparameters. This is conducted under the observation of
the network’s performance in response to distinct selectionsof hyperparameters. Afterwards the model’s performance isevaluated using the test set.
The training regimen constituted an iterative process witha total of 50 cases. Each case comprised 19 feature variables,
which were either of a categorical or a numerical type. Since
our interest was to differentiate between trading and trending
price, we required only a singular categorical response variable.
This variable was classified as 1 to denote a trending price, or 0
to signify a trading price. After training the model, the model’s
predictive accuracy was assessed by testing it against an
additional set of ten cases.
A standard neural network comprises layers ofinterconnected nodes, often referred to as “neurons”. Neuralnetworks can be used for particularly effective handling of
high-dimensional and non-linear data and find utility in both
regression and classification tasks. A classification task, suchas the one examined in the present study, typically involves theprediction of an input’s class (in this case, trending or trading
price) based on its characteristic features (in this context, thevalues of various indicators).
A three-layered neural network typically consists of an
input layer, one hidden layer, and an output layer. In the input
layer the network takes in the data for processing. The hidden
layer transforms the inputs into something that the output
layer can use. This is called “hidden” because its inputs andoutputs are masked by the activation function and the weights.
The output layer produces the final prediction or classification
result, whereas a three-layered neural network has an input
layer, two hidden layers, and an output layer. The additional
hidden layer allows the network to learn more complex
representations of the data.
The purpose of an activation function is to introduce nonlinearity into the network, allowing it to learn and represent
more complex patterns in the data. The activation function
for each neuron in the hidden layers is also discretionary. A
common choice for this purpose is the rectified linear unit
(ReLU) function, which serves to introduce an element of
non-linearity. However, when it comes to the neuron in the
output layer, to reduce overfitting we used the reserved
validation data for control of the training process. If the lossof the validation data stops decreasing, we save the adjusted
weights that lead to the lowest loss of the validation data forour model. Classification models are usually evaluated using
accuracy, precision, recall, and F1 score. These metrics provide acomprehensive assessment of the model’s performance.

2024 EDITION

Results
3.1 Hyperparameter Setting for the Neural
Network
Figure 4 The architecture of the three-layered neuralnetwork (a), with its performance percentages plottedon a so-called confusion matrix (b)IFTA.ORG PAGE 55

IFTA JOURNAL

2024 EDITIONIn the context of this study, an artificial neural network
was assessed for its performance in predicting a trend following
a breakout of the opening range, which was defined as thefirst 30 minutes after the start of the trading session of theE-mini-S&P 500 Future at the New York Stock Exchange opening
at 9:30 a.m. Eastern Time. This assessment involved various
presets of several hyperparameters, as depicted in Figure4(a). These hyperparameters included: the number of layers
within the network; the size of these layers as determined by
the quantity of neurons; a selection of an activation function(sigmoid, hyperbolic tangent, rectified linear unit); the count offeature variables as input into the model; and the strength of
regularization, represented by the parameter lambda (λ).
In the context of neural network architecture, especially
one featuring an increasing size of layers and nodes, thenetwork will be able to model more complex relationships inthe data. Generally, more neurons mean more dimensions into
which the training data can be separated. After the dimensions
have expanded, the data need to be condensed back into one
dimension because the output – in this case, future price – isexpressed along a single dimension.
A binary value (0 or 1) was chosen, based on whether the
price after the opening range was trending, encoded as 1, or
whether there occurred trading in a range (non-trending), in
which case this was encoded as 0. However, with an increasing
number of layers and nodes a binary value might also be more
likely to overfit the model. Overfitting refers to a situation
whereby a model has been trained too well and starts toperform poorly, and can occur when the model becomes toocomplex or when the training data are insufficient. The model
starts to memorize noise or specific patterns which do not
represent genuine underlying patterns in the data. Signs ofoverfitting are high accuracy during the training phase ofa model but low-quality performance on new data. To avoid
overfitting and to simplify the model, it is advisable to increase
the amount of data by applying regularization techniques, andto shorten or even curtail the training process when the model’s
performance is unstable or oscillating.
For our model a three-layered (input, hidden, output)
neural network architecture has proven to be the most effective
solution, with the input layer consisting of 19 neurons andthen the hidden layer of ten neurons. For the output layer, one
neuron was found to be the best setup. In a first step, input
data were standardized. The best activation function forachieving this was the ReLU function f(x) = max (0, x) with the
input x. If x is positive, the function returns x, and if the input
is negative, the function returns 0. = 0 was the best value
for the regularization strength. A larger value of results in astronger regularization effect and encourages the model to havesmaller weights. The optimal value achieves the best balance
between model complexity and generalization and depends on
the specific problem and the data set.
The confusion matrix, the true positive rates (TPRs) and thefalse negative rates (FNRs) of the validated model are presented
in Figure 4(b). Each row of the confusion matrix represents theactual class and each column corresponds to the predicted class.

PAGE 56 IFTA.ORG

Figure 5 ANOVA scores of different indicators (a) andaccuracy and minimum classification error (b) dependingon the number of indicators

To further refine the neural network, the number of input
variables was evaluated. In a first step, the 19 feature variables
listed in Table 1 were used as input. The input variables werethen successively reduced by two. The importance of eachfeature variable was evaluated and ranked using an analysis
of variance (ANOVA) statistical technique (Figure 5(a)). To
reduce the input variables from 19 to five further improved theperformance of the model (Figure 5). The five variables withthe greatest input were, in descending order: price in relation
to the first standard deviation band of VWAP (ANOVA = 5.25)
and in relation to the VWAP line (ANOVA = 1.11); the relationshipbetween bullish and bearish one-minute candles over the
opening range (ANOVA = 2.54); the number of high-speed
price movements during the opening range analyzed with the

IFTA JOURNAL

intra-bar price movement (IBPM) indicator (ANOVA = 2.21);
the relationship between candle size to wick size within the
30-minute opening range “candle” (ANOVA = 1.29); and the highfrequency presence (HFP) in price data during the opening range(ANOVA = 0.83).
Out of the 19 indicators featured in this study, bothindicators we had developed – IBPM and HFP – were included in
the final set of the top five indicators for predicting a trend.
The type of indicator best suited for the issue also depends
on the amount of data, the trading instrument, timeframe,
and trading hours. Figure 5(b) indicates the increase ofmodel performance in relation to the number of indicators. A
reduction of indicators leads to a more closely fitting (although
not overfitting) model. The number of indicators was reduced
successively by two and the accuracy (ACC) and the minimum
classification error (MCE) were plotted. As illustrated in
Figure 5(b), the selection of five indicators exhibits superior
performance with the highest ACC and the lowest MCE. Despite
the relatively small amount of data, the accuracy of the model
was quite high.

2024 EDITION

3.2 Prediction of the Model
Once the model had been trained, validated, and finalized,
it was used to predict a significant price move of the actual
E-mini S&P 500 Future September 2023 contract (see Table 2
in the Appendix). This topic is a typical classification task forsupervised learning when it comes to predicting the categoricalclass labels of new instances based on past observations, withthe aim of assigning an input to one of the given classes. The
network has now learnt to recognize patterns in the input
data that correlate with certain labels. The network does thisby iteratively adjusting its internal parameters to minimize
the difference between its predictions and the actual labels (aprocess known as back propagation). For a binary classification
problem, where there are only two possible classes – trending(1) or non-trending (0) – a single output neuron can be used thatwould generate a value of 0 or 1. A softmax function can be used
to convert the output into a probability distribution over theclasses.

Figure 6 Predictions of the finalized neural network, showing confusion matrix with differences between actual andpredicted values (a) and the key metrics of the neural network for predictions (b)The confusion matrix in Figure 6(a) shows the performance of the classification model to predict unseen data. Based on the four
values in the confusion matrix (true positive, false negative, false positive, and true negative), various key metrics were calculated
to assess the performance of the neural network, such as accuracy, precision, recall (sensitivity), and F1 score. For the non-trendingclass 0 the precision is 100% indicating that, for all instances classified as non-trending, these are true negative predictions. The recall
is approximately 33%, indicating that the model correctly captures 33% of all non-trending price moves. The F1 score is about 50%,
representing the harmonic mean of precision and recall. For the trending price move encoded as class 1 the precision is around 78%,
the recall is 100%, and the F1 score is about 88%. The overall accuracy of the finalized neural network is approximately 80%, whichsuggests that it correctly predicted a trend or a trading range after the breakout of the opening range of the E-mini S&P 500 Future in
about 80% of cases. The modeled network has a better recall and F1 score for a trend prediction compared to a trading range.

IFTA.ORG PAGE 57

IFTA JOURNAL

2024 EDITION

Discussion
4.1 Artificial Intelligence for Optimal Indicator
Setup
Technical analysis has a long history of widespread use bymarket participants with a large body of academic evidence
including theoretical support and empirical evidence (Rodolfo
2017, p 115). This study explored the application of a neuralnetwork for predicting a price move after the first 30 minutes atthe start of the trading session for the E-mini S&P 500 Future.
Previous studies have mainly investigated the prediction ofstock prices or ways of optimizing portfolios. By evaluating
historical data, we aim to analyze the performance of themodels in capturing trends and patterns, thereby providing
insights into the potential use of such models in making
short-term trading decisions. Various steps were involvedin the analysis, including defining an indicator combination
comprising feature variables, as well as carrying out data
preprocessing, model construction, training, evaluation, andvisualization.
In today’s fast-paced financial markets, intra-day trading
has emerged as a popular strategy for those seeking short-term
gains. With the rapid advances in technology and the growing
influence of artificial intelligence, traders are using the powerof machine learning more and more frequently to optimize theirtrading. In this fast-growing field, continuous studies need tobe performed with the aim of identifying useful applications.
We have shown that the fusion of sophisticated trading
techniques based on technical indicators in combination withthe competitive edge provided by machine learning algorithms
can be used to find simplified and clear trading strategies.
Some may argue that AI is unnecessary for trend identification
since any expert can observe a trend. This may be true to an
extent but human behaviors like risk aversion during successand risk-seeking during loss often interfere with trading. AI
can help to identify potential risks that are difficult for humananalysts to be aware of because indicators are mostly selected
for the purposes of supporting someone’s initial hypothesis.
Nowadays the ease of access to information and the increasinguse of new technologies and alternative data sources like social
media make the selection of pertinent information an ever more
complex task – especially for retail traders.
But gaining an edge is paramount for successful trading.
This is where AI can help the trader to select the most relevant
information and the best indicator setup quickly and efficiently.
We have demonstrated how to use a neural network to select thebest indicator setup from a large variety of possible indicators
for a specific market constellation, instrument, and trading
hour. The neural network tested here can be trained to recognize
patterns in a large amount of financial data, to run complex
mathematical operations, and to help inform buy-or-selldecisions in real time. Furthermore, it can operate 24/7.
But there are also several potential drawbacks like overoptimization, the risk of overtrading, loss of control, and limited
learning. If AI ends up informing everyone’s trading decisions
for them, then the market will drastically change. Further,
if an AI service is hacked, directing traders to adopt specificbehaviors, it could result in manipulation of the market. As AI
PAGE 58 IFTA.ORG

is continually evolving while its accuracy will necessarily beless than perfect, traders should be aware of this and always
rely on their own judgment when making trading decisions.
Neural networks are based on historical data that may or may
not hold true in the future. Therefore, predictions generated
by AI tools should always be used in combination with othertrading and risk management strategies. Trading relies on
speculation, diversity, and differences of opinion. So AI shouldat the moment be viewed as an aid that could make trading
more efficient regardless of what trading style is preferred,
whether completely discretionary, semi-automated or fully
automated. We hope we have demonstrated here that reducing
the number of indicators to specific feature variables canenhance a neural network’s performance. This observationaligns with the conventional advice to observe the tenet ofsimplicity when trading. As evidenced by the model’s output,
the utility of selecting various types of indicators is essential to
avoid multicollinearity of indicators. Multicollinearity can leadto unreliable trading signals because the redundant information
provided by highly correlated indicators can amplify the effectof noise and lead to an increase in the loss of interpretability.
The ranking of both the IBPM and the HFP indicators as among
the top-five performers in the ANOVA analysis supports theargument that significant price movements are often driven by
big market players and high trading activity, especially after the
opening of the trading session.
As previously argued, hyperparameter optimization(HPO) is another important step for enhancing models – evenwith a relatively scant amount of data. Other suggestions for
improving a model’s performance are: increasing the amountof training data; adding more input variables; researching moreadvanced models that can potentially capture more complex
patterns in the data; bringing feature engineering expertiseto transform the raw data into more complex data by applying
mathematical calculations; and resampling the data along
different timeframes.
In this study we introduced some methods for helping intrend detection on a one-minute and 30-minute chart from eachtrading day’s data of the E-mini S&P 500 Futures, combined with
an appropriate indicator configuration.
One limitation of this study is the small amount of data
available. While we achieved still a good accuracy in our model
predictions, it is important to consider that a larger dataset
might uncover different patterns or exceptions that ourcurrent dataset did not capture. Additionally, a small dataset
might lead to overfitting. We did not conduct back testing on
our neural network model in this study, therefore we cannot
accurately measure the real-world performance of the model,
especially considering transaction costs, slippage, and othermarket microstructure effects. Our model utilizes binaryfeature variables, quantitative feature variables might offer
more information and subsequently improve model accuracy
and interpretation. On the other hand, binary representation,although simplifying the decision-making process. Financial
markets are influenced by a myriad of external factors, ranging
from geopolitical events to economic indicators. Our model
might not have taken into account all of these externalities,
which can significantly influence trading outcomes.

IFTA JOURNAL

4.2 Practical Implications for Trading
Our research combined three themes – technicalindicators, machine learning, and trading strategy. There
are numerous trading ideas and algorithms for traders andstrategy developers that combine classic indicators with newconcepts, and this could represent a veritable goldmine for
future trading activities. In today’s world, researching andtesting fresh strategies, indicators, and trading setups isimportant for continually improving trading and for adapting
to new market structures and dynamics. Simplicity is the key tobetter real-time performance. Modern testing approaches using
machine learning and computer vision represent one possible
avenue for identifying and simplifying deployable strategies for
traders tailored to particular trading styles. AI trading offers
the capacity to process large amounts of data including multiple
indicators, news feeds, and historical price data to identify
trading opportunities. The ability to process and interpretlarge data sets quickly could eventually lead to more informed
and data-driven trading decisions. For short-term trades,
the innovative approach presented in this study offers great
potential for enhancing and refining trading strategies. A neuralnetwork is a powerful tool for helping to select an optimal
indicator setup for a specific market condition and can be highly
effective in optimizing new trading strategies for the future.

Summary
5.1 Conclusion and Future WorkIn the context of this research study, our focus has been
on evaluating the optimal indicator setup for carrying out
trades on the very liquid futures markets of the S&P 500 andto predict a short trend after the first 30-minute “candles” of atypical trading day. With our two self-developed indicators andby reducing the 19 initially chosen indicators to the five mostimportant for this special market constellation, we were able toachieve an accuracy of approximately 80% using an optimized
neural network. This result demonstrates how effectively
classic trading strategies can be combined with AI to gain acompetitive edge.
While physical phenomena are often foreseeable andfollow recognized formulas, financial data are much moreunpredictable but nonetheless amenable to modeling. But,
as the British statistician George Box noted 1976, “All models
are wrong, but some are useful.” Our intention for this work
was to combine – and thereby enhance – more traditional
trading strategies with the aid of neural networks. In due
course the authors hope to build more accurate models basedon additional data, alternative indicator configurations, theuse of different financial instruments and trading timeframes,

2024 EDITION

and more accurate back-testing. AI can help us select the
optimal indicator combination for specific market conditions
influenced by the actual economic environment, the vagaries ofmarket sentiment, and broader current events. It is a promising
approach to further develop trading because, in trading,personal experience often yields insights that raw data could
overlook. Traders should therefore always take into accountboth personal experience and data-driven models for optimal
decision-making.

References
1. Chan, Ernest P. Algorithmic Trading: Winning Strategies and Their
Rationale. 1st ed., Wiley, 2013.
2. Kumbure, Mahinda Mailagaha, et al. “Machine learning techniquesand data for stock market forecasting: A literature review.” Expert
Systems With Applications 197 (2022): 1-42.
3. McCarthy, Edward. Foundations of Computational Finance with
MATLAB. 1st ed., Wiley, 2018.
4. Steidlmayer, J. Peter, and Steven B. Hawkins. Steidlmayer on Markets:
Trading with Market Profile. 2nd ed., Wiley, 2002.
5. Warren, Anthony W., and Jack K. Hutson. “Cycle Analysis: Maximum
Entropy Optimization.” Technical Analysis of Stocks & Commodities
2:4 (1984): 123–129.
6. Calhoun, Ken. “Trading First-Hour Breakouts.” Stocks & Commodities
33:12 (2015): 20–23.
7. Shiller, Robert J. “From Efficient Markets to Behavioral Finance.”
Journal of Economic Perspectives 17:1 (2003): 83–104.
8. Malkiel, Burton G. “The Efficient Market Hypothesis and Its Critics.”
Journal of Economic Perspectives 17:1 (2003a): 59–82.
9. Fang, J, Y Qin, and B Jacobsen. “Technical market indicators: An
overview.” Journal of Behavioral and Experimental Finance 4 (2014):
25–56.
10. Chen, C.H. Handbook of Pattern Recognition And Computer Vision. 5thed., World Scientific, 2016.
11. Brooks, Al. Trading Price Action Trends: Technical Analysis of Price
Charts Bar by Bar for the Serious Trader. Wiley, 2011.
12. Nazário, Rodolfo Toribio Farias, et al. “A literature review of technicalanalysis on stock markets.” The Quarterly Review of Economics andFinance 66 (2017): 115–126.

Endnotes
U.S. Commodity Futures Trading Commission (CFTC) https://www.cftc.
gov/MarketReports/CommitmentsofTraders/index.htm

IFTA.ORG PAGE 59

IFTA JOURNAL

2024 EDITION

Appendix
Table 2 Technical analysis of opening ranges of the E-mini S&P 500 Future contract for September 2023; data used for prediction of the finalizedneural network
COT Re-port: per-centage change
to determine market sen-timent[weekly

0.17

0.12

0.29

0.08

0.22

0.44

0.16

0.22

0.16

0.44

Candleopening range:bullish bullish bearish bearish bullish bullish bearish bullish bullish bullishbullish or bearish[30min]Body-size
candle open-ing range:
small

large

small

small

large

large

large

large

small

large

-1

1

-1

-1

1

1

1

0

-1

0

1.7

0.94

0.7

1.14

1.14

1.0

0.66

1.3

1.72

1.14

0

0

-1

-1

0

-1

0

1

0

0

1

1

-1

-1

-1

1

-1

1

1

1

DD

b

D

D

D

b

D

D

D

DD

large body or small body
[30min]Relation ofbody size to wick size of the candle
opening range[30min]Ratio number ofbullish to bearish
candles overopening range[1min]
Candle opening range:
between [0], crossing above [1] orcrossing below [-1] on previous-day
high or low [30min]
Price trading:above [1] or
below [-1]
EMA 20Volume profile shape over opening
range:
D-shape,I-shape,b-shape,P-shape,double distribution (DD),non-signifi-cant shape (non)PAGE 60 IFTA.ORG

IFTA JOURNAL

2024 EDITION

Candleopening range [30min]:
1

1

-1

-1

-1

1

-1

1

1

1

1

1

0

-1

0

0

0

1

0

0

1

1

-1

-1

-1

-1

1

-1

-1

-1

0

0

0

1

0

0

0

1

1

0

0.3

0.3

0.35

0.3

0.35

0.25

0.33

0.3

0.35

0.28

FFT
short-term cycle
high frequency presence (HFP)
in volume
spectrogram [cycles/min]

0.4

0.5

0.5

0.3

0.45

0.25

0.5

0.45

0.45

0.35

Computer visionvelocity-price tracking of thenumber of impulsive high-velocity
movements[30 min]

14

17

8

9

12

13

17

14

20

13

above [1] or below [-1] VWAP line
[weekly]
Candleopening range [30min]:above [1] ,below [-1] orwithin [0] one SD
VWAP band[weekly]
Candleopening range[30min]:above [1] or below [0]POC [weekly]
Volumeopening range
in relation to average volume:large [1]= over average;
normal [0]= near average;
small [-1]= under average
FFT
short-term cycle
high-frequency presence (HFP) in
price
spectrogram[cycles/min]

IFTA.ORG PAGE 61

IFTA JOURNAL

2024 EDITION

Andrew Thrasher, CMT

The 5% Canary

Financial Enhancement Group LLC
Noblesville, Indiana USA

NAAIM Founders

athrasher@yourlifeafterwork.com

Abstract
This paper will show that the amount of time taken for the
S&P 500 or Dow Jones Industrial Average to decline by 5% froma 52-week high illustrates significant insight to the subsequent
trend in price. A study on price history for two major equity
indices is conducted to show a relationship between durationof an initial decline and the potential for further material
weakness or the opportunity for the index to reverse and movehigher. With the examination of an 18th century mathematicalchallenge, a simple lens into the market is shown and evaluated,
resulting in a tool that retail and professional investors may
apply to markets in the pursuit of capital preservation andappreciation.

Introduction
Buy the dip or prepare for further decline? That’s the question
presented to investors throughout each trading year as theequity market ebbs and flows, experiencing periods of volatility
and persistent trends. Since 1950, the S&P 500 has spent 90% of
the time in some degree of drawdown.1 The proper managementof risk is one of the cornerstones of being a successful investor
in the long-term, and to do so, a suitable discipline of buy andsell protocols must be in place. This paper focuses on the initial
5% declines from 52-week highs in the price history for the S&P
500 and Dow Jones Industrial Average to determine if the speed
at which this decline occurs has predictive value in the ensuingprice direction for the equity market. The topic will be divided
into two sections: first, the evaluation of the implications of anequity index declining by 5% within a specific period of time; andsecond, the possible bullish opportunities that may result whenthese 5% declines occur over a protracted number of tradingdays. Findings will show that the measure of time it takes thenoted equity indices to decline by 5% does have meaningfulvalue in both downside mitigation as well as in upside capture
potential.

time. While a straight line may be the shortest path between
two points, Bernoulli’s proposed question and the subsequentanswer showed it not to be the quickest.2 While it took Bernoulli
much longer than Isaac Newton, who anonymously submitted
his solution to the challenge, Bernoulli applied the findingsof Pierre de Fermat who uncovered the principle of least
time based on his work calculating refraction angles and the
trajectory light takes when traveling between two points.2
When working on the solution, Bernoulli recognize the mostefficient path used the differential equation for a cycloid, which
is simply the arc shape that would be traced if one put a pin or
writing instrument in the exact middle of a ball or wheel (anycircular object) and rolled it on an level surface.3 In Figure 1, a
depiction of the cycloid-shaped curve of the brachistochrone
curve (illustrated by the red line), we can see how the dramatic
drop and arc of the curved path allows an object to travel at
an initial high rate of speed without sacrificing a significant
distance, while an identical object traveling on the course of
the straight line moves at a slower pace. This application of acycloid in a brachistochrone curve has been used in many areas
outside of academia, including extreme sports like surfing4 andskiing.5 The idea of “early speed” in the movement of an object,
as adapted from the brachistochrone curve, will be the primary
focus of this paper and its application to the equity market.
This concept will be drawn upon to help answer the question ofwhether the initial amount of time it takes price to decline hasa relationship with the resulting drawdown experienced by anequity index.
Figure 1: The Brachistochrone Curve

Literature Review
Early Speed
The initial concept of evaluating the possible risks of amarket downturn based on the acceleration of the first signsof market weakness stemmed from this author’s research on
the brachistochrone curve. In 1696, Johann Bernoulli posed achallenge to the math community that sought to discover the
shape of the path an object must travel when being pulled bygravity to travel from point A to point B in the least amount of1
Based on closing value of the S&P 500 from January 1st, 1950 throughSeptember 30, 2022.

PAGE 62 IFTA.ORG

Source: Shi & Celik, 2017
Investor Sensitivity to Losses
Evaluating the movement in price activity of the cited indicesas they experience early signs of drawdown, an investor mustevaluate if action needs to be taken to protect from further
2
3

See Herrera, 1994
See 3Blue1Brown, 2016

See Henry & Watt, 1998
See Jennings, 2017

4
5

IFTA JOURNAL

declining market prices or if an opportunity is being presented
for the index to reverse its decline and begin moving higher. In
their paper on Prospect Theory, Kahneman and Tversky showed
the experience of loss is twice as great as the pleasure derived
from gain.6 Ultimately this impacts an investor’s ability tounemotionally make decisions in regard to avoiding further loss
and seeking capital appreciation opportunities.
Because of the overt sensitivity to losses on investors,
larger market moves can draw a greater degree of attention
as observed by Kaminski and Lo, “in particular, in the eventof a significant drop in aggregate stock prices, investors who
are generally passive will become motivated to trade because
mounting losses will cause them to pay attention when they
ordinarily would not.”7 Kaminski and Lo go on to contend
that this increase in attention can enhance the irrationalityof market participants and exacerbate the downside market
move. This focus on attention-driven behavior also impacts
buying decisions to a greater degree for retail investors. Barberand Odean note, “individual investors display attention-driven
buying behavior. They are net buyers on high-volume days,
following both extremely negative and extremely positive oneday returns, and when stocks are in the news. Attention-driven
buying is similar for large capitalization stocks and for small
stocks."8This paper will address this emotionally driven impedimentto buying in Section Two, applying a data dependent lens tobuying opportunities presented after protracted periods ofprice weakness. The emotional emphasis on attention-grabbing
data and media is also expanded with the increase in available
resources to investors. However, there seems to be a stronger
reliance on external resources for broad market viewpoints
compared to stock-specific opinions. Peng and Xiong argue thatinvestors put a greater degree of focus on broad market andsector-level information inputs than on individual stock-related
data points.9 This goes to the importance of properly evaluating
the price movement of the broad equity market indices in amore pragmatic approach.
Not only do investors over-react to large downside market
events, but they also expect them to occur more often thanhistory would suggest. A survey of high-net-worth andinstitutional investors from 1980 to 2004 found that accredited
investors placed a 19% probability of a 1929 or October 1987type of crash occurring again. Instead, from 1925 through2015 the market has experienced crash-like declines just 1.7%of the time.10 While periods of major market weakness are notabnormal, they do not occur nearly as often as many investors
believe they will. This irrational belief can be corrected byhaving a methodology for evaluating market declines early
on in their potential developing process. The approach that is
discussed in this paper is one such method, which may provide
enough advance warning to make proper investment decisions
to escape the possible pain from losses Kahneman and Tversky
have shown investors are so eager to avoid.
See Kahneman & Tversky, 1979
See Kaminski & Lo, 20148
See Barber & Odean, 2008
9
See Peng & Xiong, 2006
10
See Goetzmann, Dasol & Shiller, 2016672024 EDITION

Drawdowns & Market Timing
As previously stated, the S&P 500 has been in some form of
decline during 90% of its trading days. While we can only know
the final degree of decline after it has occurred, historicallymost down trends experienced by the S&P 500 have been
between 2% and 6%. In Figure 2 we can see that when declinesthat exceed 2% on a closing basis, 63% of drawdowns in theindex are in the noted range.11 While 2% to 6% may well bewithin the acceptable risk range for most investors, it’s thedeclines that move into the double-digit category that cause
many investors to become uncomfortable and begin to react
irrationally. This paper will present a methodology investor canuse to evaluate if the more common 5% declines in the S&P 500
and Dow Jones Industrial Average are likely to continue lower
and threaten the risk of a more severe drawdown or offer amean-reversion bullish opportunistic trade.
Figure 2: Number of Declines By Percentage Group in the
S&P 500

Percentage declines in price for the S&P 500 based on closing
values from January 1950 to September 2022 grouped into elevenbuckets. Declines less than 2% were excluded for scaling purposes.
The practice of market timing often involves the use oftechnical analysis – using the data provided by changes in priceand volume to make investment decisions in the active pursuit ofcapital appreciation and/or capital preservation. Market timing
is often viewed as the third rail of the financial industry, drawing
strong views from both adamant supporters and hardened critics.
One of the most common arguments against market timing is
the belief that potentially missing the strongest days of market
performance will have a larger cost to the investor than what
could be gained by avoiding the largest declines. This belief wasdisproven in Antoons (2016) with a review of market history from1961 through 2015, which found the annualized return for missing
the 25 best days in the S&P 500 to be 5.74% and avoiding the worst
25 days produced a return of 15.27%. However, if an investor
were to miss both the best and worst days, Antoons notes theannualized return would have been 10.94%, still exceeding that ofa buy and hold investor of 9.87%.12
During the evaluated period, 609 declines of less than 2% occurred and are outside thescope of focus for this paper.
12
See Antoons, 201611

IFTA.ORG PAGE 63

IFTA JOURNAL

2024 EDITION

The perception that markets are entirely random has also
been shown to not be accurate.13 If there is fruit to be harvested
by active involvement in financial markets through the useof timing opportune and inopportune periods of investment,
then certain methods are likely to be shown to be morequalified than others. Through the extensive testing of tools
and lookback periods, technical analysis has been shown to bean appropriate form of market research. Brock, Lakonishok
and LeBaron conducted a review of market data from 1897 to
1986, using price history of the Dow Jones Industrial Average.
They tested trading signals generated from various moving
averages and trading range breakouts, concluding that “overall,our results provide strong support for the technical strategies
that we explored. The returns obtained from buy (sell) signals
are not likely to be generated by the four popular null models.
Consistently, buy (sell) signals generate returns which arehigher (or lower) than "normal" returns.”14

indices do subscribe to Bernoulli and Newton’s concept of thesignificance early speed has on the ultimate path taken by anobject – and in this case – equity prices.
Figure 3: The Relationship Between Time to a 5%
Drawdown in the S&P 500 and Resulting Decline

Section One: The Canary Decline
Shown in Figure 2, the majority of the substantive declines
experienced in the S&P 500 are between 2% and 6%. In thisstudy, I will be narrowing the focus specifically on closing
price declines of 5%. As legendary trader and trend follower, Ed
Seykota was known for saying, “The trend is your friend except
at the end when it bends.” The bend in the trend and how quickly
it occurs is the focus of Section One. The initial 5% downward
move will be classified as the initial “bend in the trend” to bestudied in determining if the trend truly has ended.
While all investors have unique and varying degrees of risk
tolerance and time horizons, the data used throughout thispaper will be the closing daily values of a stated index obtained
from Optuma Software. The two primary indices used in the
study will be the S&P 500 and Dow Jones Industrial Average. The
S&P 500 is often believed to be the most widely tracked index
and viewed as a broad barometer of the U.S. financial market.
The Dow Jones Industrial Average, while a smaller sampling ofindividual securities, has a long history that covers multiple
market cycles.
Applying the broad concept of the brachistochrone curve andthe insights uncovered by Newton and Bernoulli, which showedthat the fastest path between two points involved early speed
in an objects decline, Figure 3 and Figure 4 show scatter plots
for the S&P 500 and Dow Jones Industrial Average, respectively.
Plotted in both figures are the number of trading days it tookeach index to decline by 5% and the resulting drawdown theindex experienced over the following six months after the initial
5% move. The declines that were 15 days or less are plottedin red. Note that the majority of the largest declines often
occurred when the index saw the initial decline develop in justthree weeks. Included are significant market events such as theGreat Depression era of the 1920s and 1930s, the Black Monday
market crash of September 1987, the inflation-induced crash of1946, the bear markets that began in 2000 and 2007, as well as
the more recent Covid Crash in 2020 and bear market of 2022.
From this look at market history, it appears equity market
13
14

See Lo & MacKinlay, 1988
See Brock, Lakonishok & LeBaron, 1992
PAGE 64 IFTA.ORG

S&P 500 closing values from January 1950 through September
2022 that resulted in a 5% decline from a 52-week high. Verticalaxis shows resulting drawdown six months following a 5% decline
from a 52-week high.
Figure 4: The Relationship Between Time to a 5%
Drawdown in the DJIA and Resulting Decline

Dow Jones Industrial Average closing values from January 1900
through March 2022 that resulted in a 5% decline from a 52week high. Vertical axis shows resulting drawdown six months
following a 5% decline from a 52-week high.

IFTA JOURNAL

2024 EDITION

Figure 5: 5% Declines From a 52-Week High in The S&P
500

In the early 20th century, canaries and other birds wereused in coal mines as early detectors of carbon monoxide.
John Haldane, an expert in respiratory physiology, is creditedwith the initial suggestion of using birds to provide an early
warning of the poisonous gas. This was due to their higher
metabolic rates compared to humans, which meant they showed
symptoms faster, such as before gas levels reached dangerous
levels to the coalminers.15 Canaries in coal mines aren’t the
only place we find unique “early warning” protocols used.
Many vineyards plant rose bushes at the ends of grapevinerows, as both roses and grapes are vulnerable to many of thesame diseases. When roses begin to show the negative signs ofa fungus, a winemaker can quickly take action to protect thegrapes.16 Just like the canary and the rose bush, the observationof a 5% decline in major equity indices, within a 15-day period,
also acts as an “early warning” of what could potentially turninto a material decline in the equity market. With that, we cantitle these developments “5% Canary” signals.
If seeking an explanation outside of 17th century
mathematics for the evident correlation between quick initialdeclines and material drawdowns, a cornerstone of technicalanalysis, the concept of momentum is well-suited for the task.
Using a classic definition of momentum, a measurement ofchange over a specified period in order to gauge the strength or
weakness of an underlying trend, shows that this accumulationof strong price action in the indices to the downside builds uponitself and draws in additional sellers, historically resulting inlarger-than-average drawdowns. However, as this paper willshow, momentum alone does not account for the separation ofoutcomes based on the time for the 5% decline to take place.
Momentum is the kindling that is lit with the proverbial matchof “early speed” in the 5% Canary signals that result in aboveaverage weakness in the equity indices.
Building on the work cited previously by Barber and Odean,
on attention-grabbing data having an impact on the emotionallydriven investor behavior, the initial 5% declines in the indicesthat occur at an accelerated rate likely garner a higher degree ofattention and with it, trade activity. The findings of Kaminski
and Lo also applies here, that the resulting declines in the equity
indices are larger than average, “…in the event of a significant
drop in aggregate stock prices, investors who are generally
passive will become motivated to trade.”8
Shown in Figures 3 and 4, a relationship for both the S&P
500 and the Dow Jones Industrial Average has been identified
between 5% Canary declines and some of the largest drawdowns
that have taken place since 1950 and 1900, respectively.
However, not all 5% Canary signals result in a steep andmaterial sell-off. As shown in Figure 5, 5% Canary signals havebeen produced throughout history, several have shown to be“ignored” by the market and no major decline has come to pass.

S&P 500 daily line chart from 1980 through November 2nd, 2022.
Red lines indicate the first 5% decline from a 52-week high thathas taken place within 15 trading days. Repeated instances within
21-days have not been shown.
The next step to be taken in the process of formalizing amethodology for using 5% Canary signals as an early warning
protocol for equities is to seek a form of price confirmation.
With confirmation, we can begin filtering the 5% Canaries thatcarry a higher degree of downside risk from those that themarket ultimately disregards. Moving Averages are common
tools used within technical analysis, with 50-day and 200-day
Simple Moving Averages (SMA) being popular lookback periods
used when technicians are applying trending identification
analysis. Moving averages are arithmetic averages of the priceof a security or index over a specified period of time. Paul Tudor
Jones also believed the 200-day SMA was a useful tool, “My
metric for everything I look at is the 200-day moving averageof closing prices. I’ve seen too many things go to zero, stocks
and commodities.”17 Siegel (2014) showed that the 200-day
SMA offers a degree of superiority to a passive buy-and-holdinvestment approach during the 1886 to 2006 period for the
Dow Jones Industrial Average. The caveat that Siegal points
out is a SMA-based market timing strategy can succumb towhipsawing markets, periods of non-trending price activity.18
Siegal is correct, when used in isolation, the obstacle to usingsmoothing mechanisms like moving averages when pricevolatility is elevated, and a trend is unable to be established. In
this paper, the usage of a moving average is applied as a formof signal confirmation rather than initial or standalone signal
generation.
Applying the 200-day SMA to the index charts we can begin
seeking affirmation of the 5% Canary signal occurrences. The
confirmation methodology is as follows:
When the underlying index declines by 5% within 15 days
from a 52-week high, (producing the 5% Canary signal), andcloses under the 200-day SMA for two consecutive days.

See Sekhar & Haldane, 2014
See Cameron, 201517
See Robbins, 201618
See Siegel, 201415

16

Going forward, these instances will be called “Confirmed
5% Canary” signals. Like many forms of analysis, whether inacademia or financial markets, validation of a hypothesis or a
IFTA.ORG PAGE 65

IFTA JOURNAL

2024 EDITION

price-based signal or indicator provides clarity and verification.
For the purposes of this paper, the consecutive closes below the200-day SMA are sought to occur within two months (42 tradingdays) of an identification of a 5% Canary signal. This period
was selected, and not optimized to avoid curve fitting, to allow
ample opportunity for price action of the index to confirm theperceived trend change as noted by the initial signal.
In Figure 6, the same chart of the S&P 500 as used in Figure
5 is shown but with the addition of red dots at the price points
when the index has closed below the 200-day SMA for two
consecutive days, providing the Confirmed 5% Canary signal.
Since 1980, there have been just 15 Confirmed 5% Canary signals
in the S&P 500 and 14 Confirmed 5% Canary signals in the Dow
Jones Industrial Average (Figure 11 in the Appendix). Included inthis sampling are the significant market events that were notedby the 5% Canary signals in Figures 3 and 4. This includes theGreat Depression, 1987 Crash, bear market following the Tech
Bubble of 2000, Financial Crisis of 2008, Covid Crash of 2020,
and the bear market that began in 2022. Of the 15 Confirmed
5% Canary signals on the S&P 500 sampling shown on Figure 6,
only four did not occur ahead of what resulted in a double-digit
drawdown for the index. Since 1980, only one drawdown of -20%
or more for the S&P 500 did not receive a Confirmed 5% Canary
signal (the bear market of 1981-1982).

Comparing the resulting price declines for the S&P 500 in
Table 1 and the Dow Jones Industrial (Table 3 in the Appendix),
both average and median drawdowns for 1-month, 3-month,
6-month and 12-month periods are shown. We can see in Figure
7 that more severe price weakness is witnessed following 5%
Canary and Confirmed 5% Canary periods compared to theentire sampling of all 5% declines that take place regardlessof length of time. For the S&P 500, the median decline 3- and6-months after Confirmed 5% Canary signals is over twice thesize of the Every 5% Decline group.
Figure 7: Comparison of Average Drawdowns Across
Various Timeframes

Figure 6: Confirmed 5% Canary Signals

Bar chart of the average drawdowns across multiple timeframes
based on S&P 500 data from January 1950 through October 2022.

S&P 500 daily line chart from 1980 through November 2nd, 2022with a 200-day SMA. Red lines indicate the first 5% decline froma 52-week high that has taken place within 15 trading days. Red
dots indicate price confirmation of 5% Canary signals based on theindex experiencing two consecutive closes below the 200-day SMA
within 42 days of the a 5% Canary signal.
Table 1: Average & Median Drawdowns For the S&P 500

S&P 500 data from January 1950 through October 2022. 5% declines are measured from 252-day closing high on the index.

PAGE 66 IFTA.ORG

IFTA JOURNAL

This decisively shows that the resulting drawdowns in equity
indices following an initial 5% decline are not solely the resultof price momentum. Instead, it shows the significance of thetime duration the decline occurs in having a larger impact on theultimate price deterioration that has historically followed.
The data for both the S&P 500 and Dow Jones Industrial
Average show outsized drawdowns for 1-, 3-, 6-, and 12-month
periods when compared to the Every 5% Decline group. Viewed
in the context of economic recessions, since 1925 there havebeen just three of the 16 NBER classified recessions that were
not first preceded by a Confirmed 5% Canary signal on either
the S&P 500 or Dow Jones Industrial Average (Figure 12 of the
Appendix). A closer look at the price history over the last six
years is also shown with 5% Canary and Confirmed 5% Canary
signals in Figure 13 of the Appendix.

Section Two: Buy The Dip
Throughout the bull market of the 1990s, traders wererewarded for buying nearly each dip in the market as stocks
charged higher month after month. This “buy the dip” mentality
bred overconfidence and helped add air to the expanding bubble
that eventually popped, resulting in the bear market that lasted
nearly three years. As human behavior often repeats itself, the“buy the dip” approach grew once again in popularity during
the decade following the Financial Crisis and intensified theyear after the Covid Crash in 2020. All good things come to an
end and the equity market showed the faults of this superficial
strategy with outsized declines that wreaked havoc on many
investors’ portfolios.
As Section One showed, 5% Canary signals provide early
warning to potential major declines in the equity market thatthen increase in confidence through Confirmed 5% Canary
signals. The next question we must ask pertains to the potential
significance of 5% declines that take longer than 15 days todevelop. One method for validating robustness of a signal isthrough the review of conditions that do not meet the statedcriteria. Section Two of this paper will look to improve upon the“buy the dip” strategy through a more quantitative approachwith a focus on when an equity index takes longer than 15 days
to experience a 5% decline.
Investors in the periods of the last 10+ years and the 1990s
were not alone in their folly of believing the dip can always bebought. Isaac Newton, considered one of the greatest minds inmathematics and physics, who also helped solve the previously
discussed Bernoulli math challenge, also was bested by themarket due to his dip buying. Newton had been drawn into the
speculation of the 1720 South Sea Company bubble and had
famously said, “I can calculate the movement of the stars, but
not the madness of men” after experiencing a severe loss when
the bubble eventually burst. Newton was one of the executorsof the Thomas Hall estate, trading in securities on its behalf,
including in South Sea Company stock. “The most interestingtransactions are the final purchases of South Sea stock, aroundthe middle of September. At that point this security was in afree fall, […] for a total of 400 stock, at prices of 520, 405, and395. They [Newton and the other executors of the trust] could
only have been motivated by deep conviction that the market’schange of heart about the South Sea Company was just a2024 EDITION

temporary irrational panic, and that there was real value inthat venture.”19 Appendix Figure 14 shows Newton’s purchases
and what we now know were failed attempts to “buy the dip”
following the summer peak in South Sea Company shares.
Identifying and respecting the long-term trend of the market
is an important first step in determining if a dip presents theproper criteria to warrant an opportunity for mean-reversion
in price. Moving averages are popular tools used in trend
identification. Similar to the confirmation criteria used in the
Confirmed 5% Canary signal of Section One, intermediate andlong-term moving averages can be used to identify up and down
trends of a respective index. Faber showed that monthly moving
averages provide superior returns in active managementof portfolios.19 In a paper published in The Journal of WealthManagement, Kilgallen showed that Simple Moving Averages
produced 28% less drawdown than a buy-and-hold strategy
for commodities, 44% less for equities, and 65% less downsidefor currencies.20 Kirkpatrick and Dahlquist also showed thatmoving averages are useful in identifying trends, “you can see
how the moving average tends to follow the trend line fairly
well. The moving average then becomes a proxy for the trendline and can be used to determine when a trend is potentiallychanging direction, just as a trend line can.”21
For the purposes of this paper, the 50-day Simple Moving
Average (SMA) above the 200-day Simple Moving Average (SMA)
will be used for classifying up trends within the index. Only
qualifying signals found on a closing basis on daily charts of
the index when the 50-day SMA closes above the 200-day SMA
will be recognized. Figures 8 and 9 show daily charts of the S&P
500 and Dow Jones Industrial Average with green arrows used
to show when the respective index has declined by 5% from a
52-week high that exceeded 15 trading days while the underlying
index was in a defined-up trend based on the above-mentioned
moving averages. Going forward, these occurrences will becalled “Buy The Dip” signals.
Figure 8: Confirmed 5% Canary & Buy The Dip Signals For
the S&P 500

S&P 500 daily line chart from 1980 through November 2022 with
Confirmed 5% Canary signals shown in red dots and Buy The Dip
signals shown in green arrows.
See Faber, 2007
See Kilgallen, 201221
See Kirkpatrick & Dahlquist, 2008
19

20

IFTA.ORG PAGE 67

IFTA JOURNAL

2024 EDITION

Figure 9: Confirmed 5% Canary & Buy The Dip Signals For
the DJIA

Table 2: Data Results from Buy The Dip and All 5%
Declines Over Various Timeframes

Dow Jones Industrial Average daily line chart from 1980 throughNovember 2022 with Confirmed 5% Canary signals shown in red
dots and Buy The Dip signals shown in green arrows.

Values based on closing values of the S&P 500 from January
1980 through June 2022. Buy The Dip based on 5% declines from
52-week highs that take more than 15 days to occur. Both Buy
The Dip signals and All 5% Decline instances were included whenoccurring in up trends based on the 50-day SMA closing above the200-day SMA.

Since 1980, the S&P 500 was higher 66.7% of the time two
weeks after Buy The Dip signals with a median gain of 2.14%,
compared to all declines of 5% within an uptrend, which
resulted in a median gain of less than 1%. As shown in Table 2,
two months after Buy The Dip signals saw the market higher
87.5% of the time with a gain of over 5.5%, compared to less than
70% for the full sample of 5% declines that saw a median gainof 3% during the same period. Alongside the improved upside
probability of the Buy the Dip signals, the range of historicaloutcomes produced a larger spread between the 80th and 20th
percentiles compared to the All 5% Decline group, offeringa more attractive risk/reward profile based on historicaloutcomes.
Figure 10: Change in the S&P 500 Following Buy the Dip
Signals & All 5% Declines

The superior risk/reward profile presented through thisnearly 42-year study on the S&P 500 shows the validity of
the Confirmed 5% Canary signal as well as the opportunities
offered when market declines are not classified as a 5% Canary.
As Albert Einstein once said, “Everything should be madeas simple as possible, but not simpler.” Section Two was not
structured on the basis of optimized data, timeframes, or signal
thresholds; criteria and structure of the studies presented wereintentionally kept simple and broad. While the focus of thispaper was on the S&P 500 and Dow Jones Industrial Average,
foreign markets were also tested, which showed similar results
as the U.S. equity indices. One distinction found with non-U.S.
indices was that the volatile nature of several less developed andemerging markets produced less meaningful signals than thelarger developed markets. Example charts of both Confirmed
5% Canary and Buy The Dip signals can be found for Germany’s
DAX Index, Japan’s Nikkei 225 Index, France’s CAC 40 Index,
Australia’s ASX Index, and Israel’s Tel Aviv 125 Index in Figures
15-19 of the Appendix.
The value of the study stands firmly in the resulting data of
the improved risk management of quick initial market declines
and in the opportunities presented to investors by index
declines that take a protracted period of time.

Conclusion

Values based on closing values of the S&P 500 from January 1980
through June 2022. Buy The Dip signals based on 5% declines from
52-week highs that take more than 15 days to occur. Both Buy
The Dip signals and All 5% Decline instances were included whenoccurring in up trends based on the 50-day SMA closing above the200-day SMA.
PAGE 68 IFTA.ORG

This paper provides a data-driven argument for using theamount of time it takes an equity index to decline by 5% toserve as either an early warning sign of a material decline in themarket or an opportunity to Buy The Dip with the assumption
the market will reverse its decline and move higher. Through astudy of market history from 1900 on the Dow Jones Industrial
Average and 1950 for the S&P 500, Figures 3 and 4 showed therelationship between the resulting drawdown and the initialdecline of the two equity indices. A relationship was found in
the observation that many of the largest drawdowns in market
history began by initially declining by 5% within 15 days. The 5%
Canary signal was improved upon with the inclusion of the 200day Simple Moving Average to assist with price confirmation

IFTA JOURNAL

of the initial signal. With a median drawdown for Confirmed
5% Canary signals of -5% after 3-months compared to -2.1%
for all 5% declines for the S&P 500 and -5.3% and -3.3% for the
DJIA, respectively, the concept of the 5% Canary proves to bemeaningful throughout market history.
The concept of measuring the time to a 5% decline was also
shown to have value in a bullish context as well, with the S&P
500 rising over 87% of the time in the two months following
a Buy The Dip signal, resulting in a 45% higher median gain
compared to all 5% declines in the S&P 500 and a 63% higher
median gain than all two month periods for the index. The
insight provided by Kaminski and Lo (2014), that investors pay
greater attention to significant declines in the market thanthey typically would, explains the need for a proper lens to view
declines such as these and to be better prepared with what
action if any should be taken.
Built upon the foundation of technical analysis research,
this study of 5% declines from both the viewpoints of bullish
and bearish market outcomes offers a unique methodology tothe investment community that can be applied by both retailand professional investors. The creation of a complete trading
strategy or system is not the objective of this paper. Analysis
on other trend classification and/or additional criteria could
be studied and tailored to the Confirmed 5% Canary and Buy
The Dip signals presented in Sections One and Two to better fit
an investor’s risk tolerance and trade preferences. Finally, theidea of the “early speed” in an object’s path that was initiallyintroduced by the creation of the brachistochrone curve in the
1700s has been shown in this paper to have robust application
to financial markets when applied to index price changes andoffers investors another tool to be deployed in both downsiderisk management and upside opportunistic applications.

2024 EDITION

Kathryn M. Kaminski and Andrew Lo, (2014), When do stop-loss rules
stop losses?, Journal of Financial Markets, 18, (C), 234-254
Kilgallen, Thomas. “Testing the Simple Moving Average acrossCommodities, Global Stock Indices, and Currencies.” The Journal of
Wealth Management 15 (2012): 100 - 82.
Kirkpatrick, Charles A., and Julie R. Dahlquist. Technical Analysis:
The Complete Resource for Financial Market Technicians. Pearson
Education, 2008.
Lo, Andrew W, and Craig MacKinlay. “Stock Market Prices Do Not Follow
Random Walks: Evidence from a Simple Specification Test.” The
Review of Financial Studies, vol. 1, no. 1, 1988, pp. 41–66., doi:https://www.jstor.org/stable/2962126.
M de Icaza Herrera, Galileo, Bernoulli, Leibniz and Newton around thebrachistochrone problem, Rev. Mexicana Fis. 40 (3) (1994), 459-475.
Odlyzko, Andrew, Newton's Financial Misadventures in the South Sea
Bubble (February 10, 2018).
Peng, Lin, and Wei Xiong. 2006. Investor attention, overconfidence andcategory learning. Journal of Financial Economics 80: 563–602.
Robbins, Tony. Money: Master the Game. Simon & Schuster LTD, 2016.
Sekhar K, Rao SC. John Scott Haldane: The father of oxygen therapy.
Indian J Anaesth. 2014 May;58(3):350-2. doi: 10.4103/00195049.135087. PMID: 25024490; PMCID: PMC4091013.
Siegel, Jeremy J. Stocks for the Long Run the Definitive Guide to
Financial Market Returns & Long-Term Investment Strategies.
McGraw Hill, 2014.

Appendix
Figure 11: 5% Canary & Confirmed 5% Canary Signals For
The DJIA

Resources
3Blue1Brown. (2016, April 1). The Brachistochrone, with Steven Strogatz[Video]. YouTube. https://youtu.be/Cld0p3a43fU
Antoons, Wim, Market Timing: Opportunities and Risks (November2016). Brandes Institute Research Paper No. 2016-06.
Barber, Brad M., and Terrance Odean. 2008. All that glitters: The effectof attention and news on the buying behavior of individual andinstitutional investors. The Review of Financial Studies 21: 785–818.
Brock, William, Josef Lakonishok, & Blake LeBaron. (1992). Simple
Technical Trading Rules and Stochastic Properties of Stock Returns.
The Journal of Finance, 47(5), 1731–1764.
Cameron, Chris. “Ask the Advisor, Roses in the Vineyards.” California
Winery Advisor, Sept. 2015, californiawineryadvisor.com/ask-theadvisor-roses-in-the-vineyards/.
Faber, Meb, A Quantitative Approach to Tactical Asset Allocation(February 1, 2013). The Journal of Wealth Management, Spring 2007
Goetzmann, William N. and Kim, Dasol and Shiller, Robert J., Crash
Beliefs from Investor Surveys (March 19, 2016).
Henry, Bruce, and Watt, Simon. “Surfing Brachistochrones.” Parabola,
vol. 34, no. 3, 1998.
Jennings, Bill. “The Physics and Mathematics of Skiing.” The Spokesman
Review, 19 Jan. 2017.
Kahneman, D., & Tversky, A. (1979). Prospect Theory: An Analysis ofDecision under Risk. Econometrica, 47(2), 263–291. https://doi.
org/10.2307/1914185

Dow Jones Industrial Average daily line chart from 1980 throughNovember 2nd, 2022, with the 200-day Simple Moving Average.
Red vertical lines indicate the first 5% decline from a 52-week highthat has taken place within 15 trading days. Red dots indicate
price confirmation of 5% Canary signals based on the index
experiencing two consecutive closes below the 200-day SMA
within 42 days of the initial 5% Canary.

IFTA.ORG PAGE 69

IFTA JOURNAL

2024 EDITION

Table 3: Average & Median Drawdowns For the DJIA

Dow Jones Industrial Average data from January 1900 through October 2022. 5% Declines are measured from 252-day closing high on theindex.
Figure 12: Recession Periods Since 1925

Figure 14: Price Chart of The South Sea Company in 1720

Dow Jones Industrial Average since 1925 and S&P 500 since1950 with NBER classified recession periods shown in gray andConfirmed 5% Canary signals shown with red dots.
Figure 13: 5% Canary & Confirmed 5% Canary Signals For
The DJIA and S&P 500
Figure 15: Confirmed 5% Canary and Buy The Dip Signals
for Australia’s XAO Index

S&P 500 and Dow Jones Industrial Average daily bar chart from2017 through October 2022. Price with 200-day Simple Moving
Average (blue line), 5% Canary (vertical red lines) and Confirmed
5% Canary Signals (red dots) shown.

PAGE 70 IFTA.ORG

Daily bar chart of XAO Index with Confirmed 5% Canary Signals in
red dots and Buy The Dip Signals shown by green arrows.

IFTA JOURNAL

2024 EDITION

Figure 16: Confirmed 5% Canary and Buy The Dip Signals
for Germany’s DAX Index

Figure 19: Confirmed 5% Canary and Buy The Dip Signals
for Israel’s Tel Aviv 125 Index

Daily bar chart of DAX Index with Confirmed 5% Canary Signals in
red dots and Buy The Dip Signals shown by green arrows.

Daily bar chart of Tel Aviv 125 Index with Confirmed 5% Canary
Signals in red dots and Buy The Dip Signals shown by green
arrows.

Figure 17: Confirmed 5% Canary and Buy The Dip Signals
for France’s CAC40 Index

Daily bar chart of CAC40 Index with Confirmed 5% Canary Signals
in red dots and Buy The Dip Signals shown by green arrows.
Figure 18: Confirmed 5% Canary and Buy The Dip Signals
for Japan’s Nikkei 225 Index

About the NAAIM Founders Award
Launched in 2009, the NAAIM Founders Award is designed
to expand awareness of active investment management
techniques and the results of active strategies through thesolicitation and publication of research on active management.
$5,000 is presented annually for the best paper submitted to thecompetition.
The National Association of Active Investment Managers(NAAIM) is a non-profit trade group of nearly 130 registeredinvestment advisor firms that collectively manage more than
$15 billion in assets. NAAIM member firms provide active money
management services to their clients to produce favorable
risk-adjusted returns as an alternative to passive, buy-and-holdinvestment strategies. NAAIM publishes the weekly NAAIM
Exposure Index and sponsors the annual Uncommon Knowledge
conference along with smaller conferences and meetings on
topics of interest to its membership. For more information, visit
www.naaim.org

Daily bar chart of Nikkei 225 Index with Confirmed 5% Canary
Signals in red dots and Buy The Dip Signals shown by green
arrows.

IFTA.ORG PAGE 71

IFTA JOURNAL

2024 EDITION

Encyclopedia of Chart Patterns by Thomas N. Bulkowski
Reviewed by Regina Meani, CFTeIn the time poor world in which we live it is so easy to press abutton for most of the things that we want. This pertains to theworld of technical analysis. Many technical analysis programs
allow us to press a button and many forms of analysis can beapplied to the chart. Some may say it is a time saver but are welosing our own individual ability to interpret the charts?
For chart interpretation, I thought that pattern recognition
was a good place to start. On my bookshelf, I found my wellworn copy of Thomas Bulkowski’s Encyclopedia of Chart
Patterns. I have the first edition and I believe it has now been
expanded with second and third editions, which add extra value
and additional features. The third edition offers 10 times thenumber of samples for statistic reporting.
Delving back into my copy, Bulkowski reminded me that“chart patterns … are the footprints of the smart money… it
pays to know what the market is thinking. It pays to follow thefootprints.”1
In the introduction, Bulkowski explains his methodology,choosing his data base, discussing the market at large,
developing an investment style and the use of theoreticalsample trades to highlight certain techniques. The body ofthe book contains detailed descriptions of over 30 patterns.
Every chapter has a heading image of the pattern for easy
identification followed by a “Results Snapshot.” Here acondensed guide serves as a quick reference. The table
includes how to identify the pattern, whether it is considered
continuation or reversal, the percentage failure rate, theaverage percentage gain or loss and the trend description.
Bulkowskis often adds a “surprising finding” as well as
associated patterns.
Each chapter is divided into sections. The “Tour” provides
a general description followed by “Identification Guidelines”
in text and in a table. Bulkowski then “Focuses on Failures,”describing what a failed pattern looks like and why they failed

PAGE 72 IFTA.ORG

and what to do when they fail.
The next section deals with the statistics and often highlights
the trustworthiness of the pattern and the potential returns.
The section on “Trading Tactics” is one of the most useful as
it sets out a guide that helps maximize profits and minimize
losses, identifying where to place stop losses and when to golong or short. Finally, in the “Sample Trade,” Bulkowski uses aunique and not without humour story telling style which takes
you step by step on how to trade the patterns. In the complex
head and shoulders trade, in Chapter 19, he ends by falling off his
bicycle.
The third edition adds to the sections in the chapters with“Experience,” which lets you share Bulkowski’s expertise,sitting at the master’s knee, learning the lessons from his
trading techniques.
Throughout the pages of this book there is a wealthof examples, which show pattern guidelines and tag theappropriate target price.
As many of us press that “button” in our analysis program,it might be useful to keep a copy of the Encyclopedia of Chart
Patterns close by as a confirmation/reference tool, and as I am
intrigued by the new additions to the third edition, I will be
updating my bookshelf.

Notes
1

Bulkowski, TN, Encyclopedia of Chart Patterns, John Wily & Sons,
Canada, 2000, pg 3

IFTA JOURNAL

2024 EDITION

Author Profiles
Andrea Bolognesi
Andrea Bolognesi is a second-year PPE & Data
Science student at University College London(UCL) and an incoming summer analyst at UBS
London. He possesses a keen interest in equities,
global macro, and quantitative as well as
systematic investment strategies. Currently, heis working towards achieving the CFA Level I certification. In
addition to his core studies, Andrea has undertaken multiple
research projects in the field of fixed income, focusing on thefactors that influence recent changes in interest rates andsubsequent market's response. Passionate about the integrationof new technologies in investment and technical analysis,
Andrea welcomes enquiries and opportunities.
Regina Meani, CFTe
Regina Meani covered world markets as atechnical analyst and associate director for
Deutsche Bank prior to freelancing. She is anauthor in the area of technical analysis and is asought after presenter both internationally andlocally, lecturing for various financial bodies anduniversities as well as the Australian Stock Exchange. Regina isa founding member and former president of the AustralianProfessional Technical Analysts (APTA) and a past journal
director for IFTA, carrying the CFTe designation and theAustralian AMT (Accredited Market Technician). She has regularcolumns in the financial press and appears in other media
forums. Her freelance work includes market analysis, webinars,
and larger seminars; advising and training investors and tradersin market psychology; CFD; and share trading and technicalanalysis. She is also a former director of the Austral-ian
Technical Analysts Association (ATAA) and has belonged to theSociety of Technical Analysts, UK (STA) for over 30 years.
Davide Pandini, PhD, CMT, MFTA, CFTe, CSTADavide Pandini holds a Ph.D. in electrical andcomputer engineering from Carnegie Mellon
University. He was a research intern at Philips
Research Labs in Eindhoven, the Netherlands,
and at Digital Equipment Corp., Western
Research Labs, in Palo Alto, U.S. He joined
STMicroelectronics in Agrate Brianza, Italy, in 1995, where he isa technical director and a fellow of ST technical staff.
Davide has authored and co-authored more than 50 papers ininternational journals and conference proceedings and servedon the program committee of several premiere international
conferences. He received the STMicroelectronics Corporate
STAR Gold Award in 2008 and 2020, and the STRIVE Gold Awardin 2022, for R&D excellence. Since June 2015, he has been thechairman of the ST Italy Technical Staff Steering Committee.
In the field of technical analysis, Davide is a Certified Financial
Technician and a Master of Financial Technical Analysis of IFTA,

holds the Chartered Market Technician (CMT) designation fromthe CMT Association, and is a professional member of SIAT
(Societa’ Italiana Analisi Tecnica). In 2021, he was the recipientof the XII SIAT Technical Analyst Award in the Open category.
He was a speaker at SIAT Trading Campus in 2022, and at theInvesting and Trading Forum in 2022 and 2023. He was thewinner of the prestigious IFTA 2021 John Brooks Memorial
Award and was a speaker at the IFTA 2023 annual conference inJakarta, Indonesia.
Davide served as volunteer at the Universal Exhibition
Expo2015—Feeding the Planet, Energy for Life—in Milano, Italy.
Andrew Thrasher, CMT
Andrew Thrasher, CMT, is the Portfolio Manager
for Financial Enhancement Group LLC andfounder of Thrasher Analytics LLC. Mr. Thrasher
holds a bachelor’s de-gree from Purdue
University and the Chartered Market Technician(CMT) designa-tion. He is a two-time winner of
the Charles H. Dow Award from the CMT Associ-ation. He wasalso a finalist in the Best Equity Research and Best Commodity
Re-search categories for the Technical Analysis Awards in 2022.
Andrew resides in Noblesville, Indiana with his wife anddaughter. His analysis has been cited by CNBC, Wall Street
Journal, MarketWatch, Bloomberg, Fox Business, ValueWalk,Yahoo! Finance, Barron’s, U.S. News, TD Ameritrade Network
and Opto.
Michael Trequattrini, CSTA
Michael Trequattrini is a quantitative
researcher specializing in alpha generation
using artificial intelligence algorithms,
developing and implementing trading andinvestment strategies across stocks, futures,and commodities. He holds a B.Sc in Bank,
Finance, and Financial Markets with Honours from the
University of Pisa and a M.Sc in Finance from the Nova School ofBusiness and Economics. He is a Certified SIAT Technical Analyst(CSTA) and the winner of the SIAT Technical Analyst Award in
2022. He has authored numerous articles and has been featured
on various YouTube channels. During his studies in Portugal, he
served as a co-portfolio manager for a local bank, actively
contributing to portfolio management.
Edzard Wiener, Ph.D, MFTA, CFTe
Member of the Vereinigung Technischer
Analysten Deutschlands e.V. (VTAD)
Dr. Edzard Wiener holds a master’s in physics
and a PhD in medicine, specializing as a Senior
Physician in Neuroradiology with a significant
focus on artificial intelligence, computer visionand neuroscience. Since 2018, Dr. Wiener has established a
specialized position for himself in the field of technical analysis.
IFTA.ORG PAGE 73

IFTA JOURNAL

2024 EDITION

He offers a unique mix of academic and practical expertisein physics, neuroscience, and trading. He has investigatedvarious aspects of market behavior, data science, artificial
intelligence, and neural networks. His intense involvement
in exploring the synergy between data science and trading
has not only expanded his professional horizon but also
contributed extensively to his success as a private trader overthe past five years. He is recognized for merging traditional
trading methodologies with cutting-edge AI and data analysis,
thereby fostering a blend of human and artificial intelligence inunderstanding market movements. His innovative indicators
offer promising avenues for understanding and predicting
significant price movements. In 2022, Dr. Wiener obtained theCertified Financial Technician (CFTe) designation and further
strengthened his credentials in 2023 by acquiring the Master ofFinancial Technical Analysis (MFTA), underscoring his profoundexpertise and commitment in technical analysis.

PAGE 74 IFTA.ORG

Christoph Wildensee, Ph.D., MFTA
Christoph Wildensee has a Ph.D. in businessadministration. He is a well-known auditor anddata/process analyst at enercity AG in
Hannover, Germany. Christoph’s special focus ison finding errors and optimization potential in
IT systems relevant to accounting, including, inparticular, the Energy Trade and Risk Management (ETRM)
system, which is used to handle all energy trading activities at
enercity. He was also a member of the team evaluating the new
Pioneer/Hitachi-ABB ETRM system.

IFTA JOURNAL

2024 EDITIONIFTA Staff

IFTA Board of Directors

Executive Director
Linda Bernetich, CAE

IFTA HEADQUARTERS
International Federation of Technical Analysts
1300 Piccard Drive, Suite LL 14
Rockville, MD 20850 USA
Phone: +1 (240) 404-6508
Fax: +1 (301) 990-9771
Email: admin@ifta.org | Web: www.ifta.org

Production Manager
Jansen VeraManaging Editor
Heather Rigby
Director of Accounting Services
Dawn Rosenfeld

President
Wieland Arlt, CFTe (VTAD)
wieland.arlt@ifta.org
Treasurer
Karin Roller, CFTe (VTAD)
karin.roller@vtad.de
Secretary and Membership Director
Warren Murnane, Dip TA, CFTe, ST & I (Wealth Within) (ATAA)
warren.murnane@ataa.asn.au
Vice President Europe, Website Director
David Watts, BSc (Hons) CEng MICE MIWEM, FSTA (STA)
Dwatts360@gmail.com
Vice President Asia-Pacific
Hiwon Yoon, Ph.D., CMTA (NTAA)
yoon@cmdlab.co.jp
Vice President The Americas, Webinar Director
Bruce Fraser (AAPTA)
rdwyckoff@me.com
Vice President Middle East and Africa
Tamer Gamal, CFTe (ESTA)
tgamal@gmail.com
Education Director
Saleh Nasser, CMT, CFTe (ESTA)
snasser72@gmail.com
Examination Director
Gregor Bauer, Ph.D., CFTe, (VTAD)
gregor.bauer@vtad.deMarketing Director
Eddie Tofpik, MSTA (STA)
Eddie.Tofpik@admisi.com
Quant Director
Giovanni Trombetta, CFTA, Electronic Engineer (SIAT)
giovanni.trombetta@gandalfproject.com
Institutional Director
Alessandro Greppi, Ph.D. (SIAT)
greppi.alessandro01@gmail.com
Non-Institutional Director
Shinji Okada, CMTA, CFTe, MFTA (NTAA)
shinjiokadaresearch@gmail.com
Development Director
Indrawijaya Rangkuti, MBA, CTA (AATI)
Indra.senna@gmail.com
Digital Media Director
Ron William, MSTA, CFTe, MSTA, CFTe (SAMT)
roniwilliam@gmail.com

IFTA.ORG PAGE 75

Official Trading Partner of the ATAA

Master the market
forces with City Index
Forex | Indices | Crypto | Commodities | Share CFDs

All trading involves risk.

Certified Financial Technician (CFTe) Program
IFTA Certified Financial Technician (CFTe) consists of the
CFTe I and CFTe II examinations. Successful completionof both examinations culminates in the award of
the CFTe, an internationally recognised professional
qualification in technical analysis.

Examinations

The CFTe I exam is multiple-choice, covering a wide
range of technical knowledge and understanding of theprincipals of technical analysis; it is offered in English,
French, German, Italian, Spanish, Arabic, and Chinese;it’s available, year-round, at testing centers throughout
the world, from IFTA’s computer-based testing provider,
Pearson VUE.
The CFTe II exam incorporates a number of questions
that require essaybased, analysis responses. The
candidate needs to demonstrate a depth of knowledge
and experience in applying various methods of technicalanalysis. The candidate is provided with current chartscovering one specific market (often an equity) to beanalysed, as though for a Fund Manager.

The CFTe II is also offered in English, French, German,
Italian, Spanish, Arabic, and Chinese, via Zoom, typicallyin April and October of each year.

Curriculum

The CFTe II program is designed for self-study, however,
IFTA will also be happy to assist in finding qualified
trainers. Local societies may offer preparatory courses
to assist potential candidates. Syllabuses, Study Guides
and registration are all available on the IFTA website at
http://www.ifta.org/certifications/registration/.

To Register

Please visit our website at http://www.ifta.org/
certifications/registration/ for registration details.

Cost

IFTA Member Colleagues
CFTe I $550 US
CFTe II $850* US

Non-Members
CFTe I $850 US
CFTe II $1,150* US*Additional Fee (CFTe II only): $100 US Proctor Fee

Master of Financial Technical Analysis (MFTA) Program
IFTA’s Master of Financial Technical Analysis (MFTA)
represents the highest professional achievement in thetechnical analysis community, worldwide. Achieving thislevel of certification requires you to submit an original
body of research in the discipline of international
technical analysis, which should be of practicalapplication.

Examinations

Timelines & Schedules

There are two MFTA sessions per year, with thefollowing deadlines:
SESSION 1“Alternative Path” application deadline February 28
Application, outline and fees deadline May 2
Paper submission deadline
October 15

In order to complete the MFTA and receive your
Diploma, you must write a research paper of no lessthan three thousand, and no more than five thousand,words. Charts, Figures and Tables may be presented inaddition.

SESSION 2“Alternative Path” application deadline July 31
Application, outline and fees deadline October 2
Paper submission deadline
March 15 (of thefollowing year)

Your paper must meet the following criteria:• It must be original• It must develop a reasoned and logical argument andlead to a sound conclusion, supported by the tests,
studies and analysis contained in the paper• The subject matter should be of practical application• It should add to the body of knowledge in thediscipline of international technical analysis

To Register

Please visit our website at http://www.ifta.org/
certifications/master-of-financial-technical-analysismfta-program/ for further details and to register.

Cost$950 US (IFTA Member Colleagues);$1,200 US (Non-Members)