Munich Personal RePEc Archive

Recursive Bands - A New Indicator For
Technical Analysis
Pierrefeu, Alex27 August 2019

Online at https://mpra.ub.uni-muenchen.de/95806/
MPRA Paper No. 95806, posted 11 Sep 2019 05:41 UTC

R ECURSIVE BANDS - A N EW I NDICATOR F OR T ECHNICALA NALYSISA P REPRINTAlex Pierrefeu
Sevilla, Dos Hermanas, 41700
shaddoll07@gmail.com

August 27, 2019

A BSTRACTIn this paper i present a new technical indicator that aim to display bands in the price chart. The bands
are calculated recursively in order to make them computationally efficient. Then various calculations
involving the bands will be described in order to provide alternatives of the proposed indicator.
Keywords Trading · Technical Analysis · Technical Indicator · Envelopes · Bands · Rescaling

1Introduction

Envelopes are a type of technical indicators that display one upper band and one lower band, they are often used todetermine possible support and resistance points when crossing with the market price, they can also determine thecurrent market trend direction when using a breakout methodology where market price is said to be up-trending whencrossing with the upper band and down-trending when crossing with the lower band. Most of the time, bands can beconstructed from µ ± kσ where µ is an estimator of the current market central tendency (SMA, EMA,...etc), σ is an
estimator of the market volatility and k a multiplicative factor. However it might be interesting to propose a recursive
method for the computations of the bands since recursion allow for more computationally efficient indicators.

2Calculation

The bands are calculated as follows :uppert = max(closet , uppert−1 ) − α|closet − uppert−1 |lowert = min(closet , lowert−1 ) + α|closet − lowert−1 |where closet is the closing market price, upper1 , lower1 = close1 and α is the smoothing factor where 1 > α > 0.
Most technical analysis software’s use an integer length as indicator parameter, therefore a potential value for α can
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be defined as α = length+1. It can be seen that from figure 1 that the bands possesses inherent smoothing which is acommon thing with envelopes indicators.
From the bands we can get a central tendency estimator basist and a volatility estimator σt each defined as :uppert + lowert
2σt = uppert − lowert

basist =A PREPRINT - AUGUST 27, 2019

Figure 1: In red uppert and lowert and in orange basist with length = 200

3Rescaling Using The Proposed Indicator

Rescaling price in a certain range is a common practice in technical analysis and various indicators aim to rescale
the closing price in a certain range (RSI[2], Stochastic[3], Williams %R[4]) . It is possible to rescale the price in anapproximate range of [0,1] by using the following formulas :x′t =closet − lowert
uppert − lowert

x′′t =

uppert − closet
uppert − lowert

or alternatively :where x′ and x′′ are the rescaled closing price.

Figure 2: In blue x′t with length = 2002

A PREPRINT - AUGUST 27, 20194Conclusion

I have presented a new method for calculating bands for technical analysis. The bands have also been used to rescale
the price a certain range. It is possible to make the proposed indicator adaptive, the efficiency ratio (ER) used in theKaufman adaptive moving average (KAMA) [1] can be a good candidate since it lays in a range of [0, 1] and decrease
when length increase, therefore for the proposed indicator could replace α with :αt′ = ERt =| closet − closet−length |Plength| ∆closet−i |i=0

Although the proposed indicator may not be profitable on the long run it could like the Bollinger bands indicator (BB)generate positive returns by using a reversal strategy [5].

References[1] P. Kaufman, Trading Systems and Methods, John Wiley Sons, Third Edition (2008).
[2] J. Welles Wilder, New Concepts in Technical Trading Systems, ISBN 0-89459-027-8[3] Lane, George M.D. (May/June 1984) “Lane’s Stochastics,” second issue of Technical Analysis of Stocks andCommodities magazine. pp 87-90.
[4] Stockcharts, Technical Indicators, Williams %R[5] Gradojevic, Nikola Lento, Camillo Wright, Chris. (2007). Investment information content in Bollinger Bands?.
Applied Financial Economics Letters. 3. 263-267. 10.1080/17446540701206576.

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