Intraday Seasonality in Efficiency, Liquidity,
Volatility and Volume: Platinum and Gold Futuresin Tokyo and New York
Kentaro Iwatsubo
Clinton Watkins
Tao XuJune 2017
Discussion Paper No.1715

GRADUATE SCHOOL OF ECONOMICS
KOBE UNIVERSITYROKKO, KOBE, JAPANIntraday Seasonality in Efficiency, Liquidity, Volatility and Volume:
Platinum and Gold Futures in Tokyo and New York

Kentaro Iwatsubo1, Clinton Watkins and Tao Xu
Kobe University, 2-1 Rokkodai-cho, Nada, Kobe, Japan 657-8501

June 2017

Abstract

We investigate intraday seasonality in, and relationships between, informational efficiency,
volatility, volume and liquidity. Platinum and gold, both traded in overlapping sessions inTokyo and New York, provide an interesting comparison because Tokyo is an internationally
important trading venue for platinum but not for gold. Our analysis indicates that both
platinum and gold markets in Tokyo are dominated by liquidity trading, while there isevidence supporting both liquidity and informed trading in New York. Separating global
trading hours into Tokyo, London and New York day sessions, we also find that liquidity
trading is more prevalent during the Tokyo day session while informed trading dominates the
New York day session for both metals in both locations. This evidence suggests that futures
markets for the same underlying commodity on different exchanges have different
microstructure characteristics, while both informed and liquidity traders choose when to tradedepending on market characteristics in different time zones.

JEL classification: G14, G15, Q02
Key words: intraday patterns, microstructure, efficiency, commodity futures

1

Corresponding author. Email address: iwatsubo@econ.kobe-u.ac.jp
11. Introduction

Why do multiple exchanges that trade the same commodity exist? A number of futures
exchanges have extended their trading hours to include night sessions, overlapping with eachother. It is now common for different exchanges to trade futures based on the sameunderlying commodity at the same time. Arbitrage activity, assisted by the globalisation ofcommodity markets and advances in trading technology, encourages commodity futures midprices on different exchanges to be virtually identical after adjusting for contract
specifications and exchange rates. A straightforward argument would suggest that market
participants prefer to trade on the exchange with superior price discovery, efficiency andliquidity. Therefore, trade in the futures of a particular commodity would be expected toagglomerate to one exchange, as higher liquidity and scale economies encourage traders to
the venue. However, multiple futures exchanges persist for many commodities.

In this paper, we aim to shed light on why this may be the case. We investigate whether
markets for commodities futures contracts on different exchanges have different
microstructure characteristics. Such differentiated characteristics may be advantageous forcertain investors, and provide a competitive advantage for the exchange. We address thisquestion by estimating and comparing the intraday seasonality of informational efficiency,
volatility, volume and liquidity in platinum and gold futures traded in overlapping sessions
on exchanges in Tokyo and New York.

Platinum and gold futures are traded on the Tokyo Commodity Exchange (TOCOM), while
in New York, platinum futures are listed on the New York Mercantile Exchange (NYMEX)
and gold on the Commodity Exchange, Inc. (COMEX). Historically, TOCOM has been an
important global venue for trading platinum futures. In the past, activity in the global market
for platinum has been heavily influenced by the hedging trades of large industrial end
consumers of platinum metal in Japan who access the futures market via TOCOM. Until
recently, the total weight of platinum represented by futures traded on TOCOM far
outweighed that of NYMEX. In 2008 for example, 3.5 million kilograms was traded on
TOCOM2, or 4.4 times that of NYMEX. However, annual volume on the Tokyo market has
been in long-term decline, down from over 16 million contracts in 2001 to just over 3.1
2

Refer to http://www.tocom.or.jp/historical/dekidaka.html for TOCOM trading volume.
2

million contracts in 2016 (including both the platinum standard and mini contracts). In 2015
NYMEX was about 2.9 times larger than Tokyo by weight of platinum, and 4.2 times larger
in 2016. However, in terms of contract volume, monthly turnover in Tokyo usually exceedsthat of New York (see Figure 1). The TOCOM contract unit is 500 grams or 16.08 troy
ounces of metal for the standard future and 100 grams for the mini contract, versus the
NYMEX standard specification of 50 Troy ounces3. Despite the decline in TOCOM volume,a not insubstantial share of the global platinum futures trade still occurs on the exchange.
Important end users of physical platinum continue to use TOCOM futures for hedging.
Global futures trade in platinum is concentrated on the two venues TOCOM and NYMEX.
This contrasts with gold, for which TOCOM’s annual futures turnover by weight of metal issmall compared to that on COMEX. As also shown in Figure 1, COMEX gold turnover by
number of contracts still dwarfs that on TOCOM despite the COMEX contract being 100 troy
ounces compared with 1 kilogram or about 32.15 troy ounces for the TOCOM standard
contract. Gold pricing is considered driven by global risk and monetary factors, and trading isdecentralised (Hauptfleisch et al., 2016). Further, there are no features of the gold business inTokyo that would suggest the location is particularly important in the determination of global
gold futures prices. Tokyo gold futures trade represented about 6 percent and 5 percent of
COMEX trade by weight in 2015 and 2016, respectively. Accordingly, platinum and gold
futures traded in Tokyo and New York provide an interesting comparison for the analysis of
intraday microstructure patterns.

TOCOM has become a more internationalised market over time. Trade orders originating
outside Japan have been an increasing proportion of total trade on TOCOM since May 2009
after the exchange launched a new trading platform and night session (TOCOM, 2015).
International buy and sell orders make up a substantial portion of both the platinum and gold
trade on TOCOM during our sample period4. Foreign buy and sell trades in the platinum
market made up approximately 36 percent and 45 percent of the total in 2014 and 2015,
respectively. The proportion of foreign transactions in the gold market was higher, with 46
3

TOCOM contract specifications can be found at
http://www.tocom.or.jp/guide/youkou/platinum.html andhttp://www.tocom.or.jp/guide/youkou/gold.html, NYMEX at
http://www.cmegroup.com/trading/metals/files/platinum-and-palladium-futures-andoptions.pdf, and COMEX at
http://www.cmegroup.com/trading/metals/precious/gold_contractSpecs_futures.html.
4
Data on foreign customer transactions is obtained fromhttp://www.tocom.or.jp/jp/historical/download.html.
3and 51 percent of both buy and sell trades in 2014 and 2015, respectively. Most foreign
orders over this period originated from the United States, Australia, Singapore and Hong
Kong.

An important difference between the Tokyo and New York futures markets for both platinum
and gold is the most actively traded maturity. In New York, as with most commodity futures
markets, nearby contract months are the most actively traded, while deferred contract months
tend to be inactively traded. As noted in Kang et al. (2011), platinum and gold in Tokyo are
actively traded in deferred contract months and inactively traded in nearby contract months.
Our analysis uses data for the most liquid contract month for each metal on each exchange.
Accordingly, we use the nearby contract months for platinum and gold in New York, and thedeferred contract months for platinum and gold in Tokyo. Although this introduces a maturity
mismatch, we do not believe this makes a material difference to our analysis. We areinterested in comparing the microstructure characteristics of the most actively traded contractfor each metal and exchange. Tokyo platinum contract trading volume in the deferred
contract exceeds that of New York in the nearby and the deferred contracts (Kang et al. 2011).
Indeed, part of the differentiation between exchanges that may be advantageous to a tradertransacting in Tokyo is the longer horizon on a market with reasonable liquidity.

Tokyo conducts an evening trading session that runs in parallel with most of the New Yorkday session. New York is also open for trade during the Tokyo day session. Do these markets
follow their own distinct intraday patterns in efficiency, liquidity, volatility and volume, or
do they have a common seasonality? Do relationships between microstructure characteristics
suggest informed or liquidity trading on these exchanges? We estimate a regression model for
intraday seasonality in each microstructure characteristic for each metal on each exchange,
and use the estimates to investigate the extent to which the markets on each exchange follow
a common intraday seasonal pattern. We also analyse the intraday relationships between
informational efficiency and return volatility, trading volume and liquidity for indications on
the prevalence and patterns of informed versus liquidity trading in the platinum and gold
markets.

We find similarities in intraday informational efficiency and return volatility patterns
between futures for the same metal traded on different exchanges, and differences in volume
and liquidity patterns. Relationships between these patterns suggest that, over global trading4

hours, the Tokyo markets for platinum and gold are dominated by liquidity trading, while
there is evidence of both liquidity and informed trading in New York. During Tokyo’s
daytime session, the markets for platinum and gold in both Tokyo and New York display
liquidity trading characteristics. Conversely, both markets for both metals havecharacteristics consistent with informed trading over the hours of New York’s daytime
session. Our analysis suggests that both informed and liquidity traders choose when to tradedepending on market characteristics in different time zones.

The paper proceeds as follows. In the next section, we summarise relevant literature on
intraday patterns in informational efficiency, volatility, volume and liquidity in financial
markets, and the intraday relationships between informational efficiency and volatility,
volume and liquidity. In section three, we describe our platinum and gold data and theregression model. In section four, we present and discuss our empirical results, and section
five concludes.

2. Review of Previous Research
2.1. Intraday Seasonality
Researchers have long sought to confirm the existence of intraday seasonality in security
prices and explain persistent intraday patterns in market microstructure characteristics such as
return volatility, trading volume and liquidity. Most studies conducted during and after the
1990s analyse intraday patterns over the daytime trading sessions in equity markets, while
few studies examine those in commodity markets.

Intraday trading volume and return volatility are typically characterised as following a Ushaped pattern in empirical studies. Both volume and volatility tend to be relatively high at
market open, relatively low for most of the trading day, and rise into the close. Equity return
volatility is shown to have a U-shaped pattern over the day in Harris (1986), Lockwood andLinn (1990), McInish and Wood (1990a), Werner and Kleidon (1996) and Abhyankar et al.
(1997). Similarly, equity trading volume has an intraday U-shaped pattern in Jain and Joh(1988), McInish and Wood (1990b), Brock and Kleidon (1992) and Chan et al. (1995).
Intraday patterns have been described as a reverse-J for some markets, where volume orvolatility ahead of the close remains substantially lower than at the open but higher than forthe middle of the trading day. Hussain (2011) reports a reverse J-shaped pattern in DAX
index return volatility, while Harju and Hussain (2011) show the same type of pattern in5other European equity indices. Further, L-shaped patterns have been observed in markets
where volume or volatility fails to rise at the end of the trading day, such as for trading
volume in DAX30 equities (Hussain, 2011). Abhyankar et al. (1997) report an M-shaped
pattern for trading volume in UK stocks.

Bid-ask spreads, a proxy for market liquidity, have also been shown to exhibit intraday Ushaped or reverse-J patterns. Brock and Kleidon (1992) find U-shaped bid-ask spread patterns
in US equities, while Ahn and Cheung (1999) and Ahn et al. (2002) discover U-shaped
patterns in Hong Kong and Japanese equities, respectively. Theissen and Freihube (2001) andHussain (2011) document reverse-J shaped intraday bid-ask spread patterns in German
equities, while Abhyankar et al. (1997) find the same shape in UK equities. Although
McInish and Wood (1992) provide evidence of a reverse-J pattern in New York Stock
Exchange bid-ask spreads, they describe it as relatively crude.

Less research has been conducted on intraday patterns in commodities and other exchange
traded asset classes. Eaves and Williams (2010), one of the few papers to analyse intraday
patterns in a commodity markets, observe U-shaped intraday volume and L-shaped return
volatility on the Tokyo Grain Exchange. Cyree and Winters (2001) find reverse-J intraday
patterns in return variances and volume in the US Fed Funds market. Their results suggest
this pattern is the result of trading stoppages rather than activity clustering around thetransactions informed traders.

Foreign exchange markets trade continuously, and despite being an over-the-counter market,
provide a close analogy in terms of trading hours to the markets we analyse in this paper. The
full TOCOM trading day that we refer to as global trading hours includes the Tokyo day
session plus the night session, and spans the normal working hours of Tokyo, London andmuch of New York. Most research on intraday patterns in currencies has focussed on return
volatility and bid-ask spreads, for example, Bollerslev and Domowitz (1993) and Hsieh andKleidon (1996). Ito and Hashimoto (2006) analyse intraday seasonality in quote revision
frequency, trading volume, return volatility and bid-ask spreads for the USD/JPY andEUR/USD exchange markets over a 24 hour trading day, and describe intraday patterns
during Tokyo, London and New York working hours. They find that quote revision
frequency, trading volume and return volatility co-move, while spreads move in the opposite
direction. Contrary to what is normally expected in equity markets, bid-ask spreads are low
6when volatility is high. Given that Tokyo hours overlap with London, and London hours
overlap with New York, but New York hours do not overlap with Tokyo, U-shaped patterns
in trading volume exist during Tokyo and London working hours, but not New York. There isno increase in activity at the end of New York working hours. Overlapping business hours
appear to boost market activity and inter-regional transactions.

2.2. Relationships between microstructure characteristics
Researchers have also examined the intraday relationships between market microstructure
characteristics. In particular, patterns of intraday informational efficiency may be correlatedwith intraday patterns in return volatility, trading volume and market liquidity. Theoreticalexplanations in the literature justify both positive and negative signs on these correlations
based on whether transactions in the market are those of informed or liquidity traders. A
variety of empirical evidence has been generated to support both interpretations.

Informational efficiency and return volatility may be related positively or negatively. The
efficient markets hypothesis suggests that return volatility results when new information
randomly hits the market. Volatility indicates the adjustment of prices to new information,and in that sense, is associated with informational efficiency. Alternatively, behaviouralists
propose that volatility cannot be explained exclusively by changes in fundamentals. Noise
traders transact irrationally, which leads to volatility in returns. Empirical studies suggest
noise traders contribute to a substantial portion of volatility in asset price returns, for example,
Shiller (1981), French and Roll (1986) and Schwert (1989). Informational efficiency andreturns volatility should be negatively related if volatility resulting from the activities of noise
traders dominates.

There are also two views regarding the relationship between volume and informational
efficiency: the “asymmetric information view” and the “inventory control view”. The
asymmetric information view argues that trades are more informative when trading volume ishigh, while the inventory control view holds that trades are less informative when trading
volume is high. Theory admits both possibilities, depending on the posited information
structure.

To understand the asymmetric information view, consider the model of Admati and
Pfleiderer (1988). To minimize their losses to informed traders, discretionary liquidity traders7

prefer to trade when they have little impact on prices. More liquidity trading in a given period
encourages informed traders to transact at the same time as liquidity traders. Competition
among informed traders reduces their total profit, benefiting liquidity traders and encouraging
their further participation. An increase in the number of informed traders contributes to more
informed prices because they cause prices to adjust faster to information. In this situation,
trading volume and the informational efficiency of prices are positively related.

Alternatively, trading volume and efficiency may be negatively related. Liquidity traders
adjust their positions from time to time. Market makers operate in commodity futures
markets, and as part of their normal business activities, unavoidably take on positions they
desire to shed immediately. The representative model of the inventory control view,
developed by Lyons (1997), relies on hot potato trading – passing unwanted positions fromdealer to dealer following an initial customer order, which reduces the informativeness ofprices. Information aggregation by dealers occurs through signal extraction applied to orderflow. The greater the noise relative to signal, the less effective signal extraction is. Passing
hot potato trades increases the noise in order flow and dilutes informational content. Hence,
trading volume and the informational efficiency of prices are negatively linked.

Theoretical arguments and empirical evidence also relate market liquidity with informational
efficiency. Two views propose alternative signs for the relationship. The “transaction costview” of liquidity can be described as the situation where greater market liquidity reducestransactions costs for informed traders, and their trades contribute to informational efficiency.
Illiquid markets imply high transactions costs for informed traders and thus are less efficient.
Kyle (1985) develops a model where an increase in liquidity leads informed traders to takemore risk on existing information, and provides greater incentives for informed traders togain more accurate information. Recent papers provide empirical support for the view that
security mispricing is greater in illiquid markets (Sadka and Scherbina, 2007; Chordia et al.,2008). Payne (2003) demonstrates that in the USD/DEM market, high volume and liquidity
periods are associated with relatively low price response, suggesting volume and liquidity are
positively related to informational efficiency.
Alternatively, the “noise trader view” says that liquidity may be a proxy for uninformed
trading and thus is associated with informational inefficiency. As a representative empirical
paper to support this view, Tetlock (2007) uses data from short-horizon binary outcome
8securities traded in online exchanges to show that the most liquid securities markets exhibit
significant pricing anomalies.
3. Data, Variables and Model
3.1. Data
We use 1-minute intraday bid and ask futures prices and trading volume for platinum andgold futures contracts. The Tokyo prices for both metals are from TOCOM, while the New
York prices for platinum are from NYMEX and those for gold are from COMEX. The
TOCOM data was purchased directly from the exchange. COMEX and NYMEX data was
obtained from Thomson Reuters. The sample spans 128 trading days from 1 September 2014
to 31 March 20155. We use the most traded contract on each exchange, which is the deferred
contract for each metal on TOCOM and the nearby contract in New York. Transactions aredenominated in Japanese yen on TOCOM, and in U.S. dollars on COMEX and NYMEX.
Our analysis is conducted based on the times of TOCOM’s trading sessions. The TOCOM
daytime trading session begins at 9:00 Japan Standard Time (JST) and ends at 15:15. After abreak, the night session begins at 16:30 and ends at 4:00 the next morning6. We refer to the
day plus the night session as global trading hours, which has a total of 1065 minutes of
trading. Accordingly, we have 1065 one-minute price and volume observations for eachtrading day or set of global trading hours. We divide TOCOM’s day and night session intonine non-overlapping time intervals denoted TI1 to TI9. TI1 to TI3 represent TOCOM’s
daytime trading session, and TI4 to TI9 represent TOCOM’s night session. The daytime
intervals are 125 minutes in duration, while the night intervals are 115 minutes long. Table 1
shows the JST, London (GMT) and New York (EST) times for each interval. We adjust forsummer time as also shown in Table 1. We refer to TI1 to TI3 as the Tokyo day session, TI4
to TI6 as the London day session, and TI7 to TI9 as the New York day session. In total, oursample contains 1152 time intervals, comprising nine intervals per day for 128 trading days.
5

General financial market conditions during our sample period could be described as typicalfor markets following the global financial and European sovereign debt crises. Market
volatility according to the Chicago Board Options Exchange VIX was elevated at times, but
not extreme, due to news such as the Bank of Japan’s surprise decision to extend its
Qualitative and Quantitative Easing program, weak economic data from Europe and China,
and the snap presidential election in Greece.
6
TOCOM extended its trading hours on 20 September 2016, after the sample period for ourstudy. The day session opens 15 minutes earlier at 08:45 JST, and closes at 15:15. The newnight session is 90 minutes longer, and runs from 16:30 to 05:30 the next day (TOCOM,
2016).
9

We calculate observations for the variables discussed in the following section for each of the1152 time intervals, and this is the data we use in our linear regression model and for ourcorrelation analysis.

3.2. Variables
We are interested in comparing market efficiency, volatility, volume and liquidity
characteristics and relationships between the markets in New York and Tokyo. Accordingly,
we construct five relevant variables from our intraday price and volume data for each of thefour futures contracts: TOCOM Platinum, NYMEX Platinum, TOCOM Gold and COMEX
Gold. The five variables are Lo and MacKinlay’s (1988) variance ratio (VR), realised
volatility (Vol), trading volume (TV), quoted half-spread (Sp), and Amihud’s (2002) measureof illiquidity (ILLIQ). The prices used in constructing the variance ratio, realised volatility,
spread and illiquidity are in local currency terms. Fluctuation in the U.S. dollar / Japanese
yen exchange rate means that the variance ratio and realised volatility of a metal will not be
equal across exchanges. The variables are defined as follows.

Lo and MacKinlay (1988) use a ratio of variance estimators to provide evidence against
random walks in stock price formation. They note that an important property of a random
walk is that the variance of the increments of the random walk is a linear function of theobservation interval of the increments. Returns that do not adhere to this property suggest thatprices are not formed according to a random walk. The distance of Lo and MacKinlay’s(1988) variance ratio from one indicates relatively greater informational inefficiency due tothe existence of either positive or negative serial correlation in the returns.

We compute the variances of 1-minute and 5-minute continuously compounded (log) returns,
rt, for mid-quote prices as defined below in equations (1) and (2), respectively. The subscriptt refers to time in minutes.
𝑟𝑡 = ln 𝑝𝑡 − ln 𝑝𝑡−1

(1)

𝑟𝑡 (5) = ln 𝑝𝑡 − ln 𝑝𝑡−5(2)

We define our statistic as the absolute value of one minus the variance ratio, since we areinterested in departures from a random walk in either direction, according to the formula in10

equation (3). The total number of minutes during each time interval, denoted as T, is equal to
125 and 115 minutes for the TOCOM day and night sessions, respectively. The term  isdefined as the mean one-minute return over the time interval. Equation (3) is interpreted as ameasure of inefficiency.
1∑𝑇 (𝑟 +𝑟 +⋯+𝑟𝑡−4 −5𝜇)2
𝑉𝑎𝑟[𝑟𝑡 (5)]T−5 𝑡=5 𝑡 𝑡−1
𝑉𝑅 = |1 − 5∗𝑉𝑎𝑟[𝑟
|
=
|1
−
|
5
2
∑𝑇
𝑡]
𝑡=1(𝑟𝑡 −𝜇)

(3)

𝑇−1

Realised volatility (Vol) in each time interval is constructed using returns based on mid-quote
prices to reduce spurious volatility due to bid-ask bounce. We multiply squared one-minutereturns by 1065, representing the total number of minutes in global trading hours. Volatility
is interpreted as daily percentage volatility during the time interval.

1065

𝑉𝑜𝑙 = 100√ 𝑇 ∑𝑇𝑡=1 𝑟𝑡2(4)

Trading volume (TV) represents the average number of contracts traded per minute in eachtime interval. Ct represents the number of contracts traded on the relevant exchange during
each minute t of our sample.
1

TV = T ∑Tt=1 𝐶𝑡(5)

We gauge market liquidity using two different approaches. The quoted half-spread (Sp) is
defined as follows.

1000

𝑝𝑎𝑠𝑘 −𝑝𝑏𝑖𝑑𝑡𝑡
𝑆𝑝 = 2𝑇 ∑𝑇𝑡=1 ((𝑝𝑎𝑠𝑘)+𝑝𝑏𝑖𝑑 )⁄2
𝑡

(6)

𝑡

In addition, we construct the measure of illiquidity (ILLIQ) suggested by Amihud (2002),
and referred to as Amihud’s ILLIQ. This measure can be thought of as quantifying thesensitivity of returns to trading volume. The more illiquid a market is, the greater is theimpact of a particular level of trade volume on a security’s return. It is calculated as anaverage for each time interval of the absolute value of 5-minute returns (𝑟𝑡 (5)𝑘 ) divided by
5-minute trading volume by weight of metal in kilograms (Vk) for futures contract k. Using

11

weight of metal in the denominator facilitates comparison between New York and Tokyo on
an amount of metal basis. We use 5-minute returns, as quoted prices do not always change
within each minute.
5

𝑇/5 |𝑟 (5) |𝐼𝐿𝐿𝐼𝑄 = 106 × 𝑇 ∑𝑘=1 𝑡𝑉 𝑘

(7)𝑘

3.3. Analysing intraday seasonality and microstructure relationships
We employ two approaches to analyse the intraday patterns and relationships between
informational efficiency and volatility, volume and liquidity. Estimates from a linear
regression model for each microstructure variable are used to characterise intraday seasonalpatterns in each futures market, controlling for daily effects. We also examine Pearson
correlation coefficients between the intraday informational efficiency and volatility, volume
and liquidity variables for global trading hours as well as the Tokyo, London and New Yorkday sessions.

We estimate the linear regression model represented by equation (8) for each of the five
microstructure variables defined above: the variance ratio (VR), realized volatility (Vol),
trading volume (TV), quoted half-spread spread (Sp), and Amihud’s ILLIQ (ILLIQ).
𝑦𝑘,𝑖,𝑗 = 𝛼𝑘,1,1 + ∑9𝑖=2 𝛽𝑘,𝑖 𝑇𝐼𝑖 + ∑128
𝑗=2 𝛾𝑘,𝑗 𝐷𝐷𝑗 + 𝜀𝑘,𝑖,𝑗(8)

One regression model is estimated for each microstructure variable and futures contract
combination. The dependent variable yki,j is the microstructure variable for futures contract k
at time i,j, where i refers to the time interval and j to the day. We regress the dependent
variable on an intercept (k,1,1), dummy variables for the time intervals (TIi) for i equal to two
to nine (TI2 to TI9), and daily dummy variables (DDj) for each of the j days in our sample
from day two to day 128.
The k,1,1 and k,i estimates are used to represent intraday seasonal patterns in the particular
microstructure variable for contract k. The estimate for k,1,1 represents the first time intervalon the first trading day, and those for the k,i represent the differential to k,1,1 for each timeinterval of the day. The daily dummies are included to account for day effects, which control
for to preclude large shocks from influencing intraday patterns and increasing correlations

12

between variables. Our results do not change substantially if the daily dummies are omitted
from the model. The model is estimated by ordinary least squares.

4. Empirical Results
4.1. Summary statistics
Summary statistics for each variable are shown in Tables 2.1 and 2.2 for platinum and gold,
respectively. Statistics for the variables related to contracts on TOCOM are denoted “TY”,
and those relating to contracts on the New York exchanges are denoted “NY”. The mean andmedian variance ratio statistics for both platinum and gold are lower in New York thanTokyo, suggesting that the New York markets are more efficient on average. Realised
volatility in Tokyo is on average lower than in New York for both metals, however the
distribution of realised volatility for Tokyo is much more leptokurtic. Tokyo platinum mean
and median trading volume exceeds those of New York in contract terms, and aresubstantially more variable. New York dwarfs Tokyo in trading volume for gold. The averageof the bid-ask spread measures in the platinum markets are similar over the two exchanges,
although Tokyo spreads appear tighter and less variable but with greater likelihood of
extreme observations. The average spread on gold is much higher in Tokyo than in New
York. For platinum, Amihud’s ILLIQ tells a different story to the bid-ask spread, suggestingthat the Tokyo market is notably less liquid than New York, since the measure normalises bytrading volume in weight of metal. Both Amihud’s ILLIQ and the spread suggest that gold
market liquidity is substantially greater in New York than Tokyo.

4.2. Intraday Seasonality
Figures 2.1 to 2.5 show the intraday seasonal patterns for each microstructure variable andfutures contract combination implied by the estimates from equation (8). The intraday
seasonal pattern estimates are k,1,1 for TI1 and the sum of k,1,1 and the appropriate k,i for
TI2 to TI9. The left pane of each figure shows the estimates for platinum and the right paneshows those for gold. Tables A1.1 and A1.2 in the Appendix show the regression estimates,
their statistical significance, and the adjusted coefficient of determination for each regression.

The estimates for the variance ratio models (see Figure 2.1) suggest that the first time intervalof the day, TI1, is by far the least informationally efficient period of global trading hours inboth the platinum and gold markets on both exchanges. Inefficiency peaks again in TI4

13

during the open of the London day session, albeit at a lower level than at the beginning of theTokyo day. In contrast, the open of the New York day session (and immediately prior) is arelatively efficient time for both platinum and gold on both exchanges. The Tokyo andLondon day sessions are similar in that at the open the markets are relatively inefficient andare relatively more efficient later in their respective sessions. Conversely, the New York day
session is different in that the market is relatively efficient at the open and is less efficientlater in the session. Over global trading hours, the evolution of the variance ratio model
estimates loosely resemble a W shape for each of the markets. Inefficiency rises at the end of
the trading day in all of the markets, particularly in platinum on both the Tokyo and New
York exchanges. While Tokyo appears marginally less efficient than New York in theplatinum market over most of global trading hours, this differential between exchange
efficiency is notably greater in the gold market, particularly after TI1.

Figure 2.2 shows the estimates for the realised volatility models. These peak at the open of
the Tokyo, London and New York day sessions for each market. Tokyo and New York open
(TI1 and TI7, respectively) are the most volatile times. After the open, volatility during theTokyo day is relatively low for both metals on both exchanges. Over global trading hours,
volatility follows a U-shaped pattern over TI1 to TI4, and then rises into the New York open
and then falls in an inverted U-shaped pattern from TI5 to TI9. During the Tokyo, London
and New York day sessions, intraday volatility takes an L-shape in Tokyo hours, a U-shape
in London hours, and declines in a linear fashion through New York hours. Patterns acrossthe two metals are similar, while volatility is greater on the New York exchanges during mosttime intervals, and particularly during the New York day session.

The intraday patterns indicated by the estimates from the trading volume models (see Figure2.3) show greater differentiation across the four metal-exchange combinations than is thecase for the variance ratio and realised volatility. In the markets for both metals, trading
volume on each exchange is concentrated during that exchange’s day session. Most platinum
trade in Tokyo occurs soon after the open of the Tokyo trading day during the first timeinterval (TI1), when the market is at its least efficient and volatility is at its highest level.
Platinum volume in Tokyo over the Tokyo day session is greater than the volume in Tokyo
during either of the London or New York day sessions. Similarly, most platinum trade on the
New York exchange occurs during the New York day session. Tokyo trading volume exceeds
New York trading volume from TI1 to TI5, while the opposite is true from TI6 to TI9.
14

During each of the Tokyo and London day sessions, TOCOM trading volume follows areverse J-shaped pattern, but during the New York day session Tokyo trading volume falls
off after peaking at the New York open. Gold trading volume in New York peaks at the New
York open, and is at a relatively high level from TI6 to TI9. New York’s trading volume ingold is far greater than Tokyo’s, and trading volume in Tokyo fluctuates less over the ninetime intervals.

The estimates for the spread regressions, shown in Figure 2.4, broadly trend up over global
trading hours (TI1 to TI9) for platinum and gold in Tokyo. Spreads on platinum in New Yorkare at their lowest during the New York day, while New York gold spreads are relatively
stable over the day. Estimates for the gold spread equations vary noticeably less than for
platinum. Also in the platinum markets, the estimates for the spread models are clearly lower
during each exchange’s day session, and higher otherwise, which makes sense as spreads
would be expected to be lower during higher trading volume periods. The estimates for
TOCOM are lower during TI1 to TI3 and higher thereafter, while spreads are lower over TI7
to TI9 for the New York exchange. Consistent with the relative importance and relative
trading volume of Tokyo and New York in the global gold market, the estimates for spread inTokyo are much larger than (about double) those for New York. In contrast, platinum spread
model estimates for Tokyo are lower than those on New York during the Tokyo day session,
while this situation reverses during the New York day session. During the London day
session, platinum spread estimates for the Tokyo and New York exchanges are about thesame.

Our estimates for the ILLIQ models are shown in Figure 2.5 and display more intraday
variation, telling a more interesting story about intraday liquidity than the estimates from the
spread models. The ILLIQ estimates show that each exchange is more liquid during its own
day session. While the Tokyo platinum market is more liquid than New York during theTokyo day, from TI5 onward New York is the more liquid market. In contrast, the Tokyo and
New York gold markets start global trading hours at about the same level of liquidity, after
which the Tokyo market becomes more illiquid while the New York market becomes more
liquid.

15

4.3. Relationships between microstructure characteristics
Tables 3.1 and 3.2 show the correlations between the variance ratio variable and each of
return volatility, trading volume, spread and ILLIQ, for platinum and gold, respectively. We
reverse the signs of the correlations between the variance ratio and both realised volatility
and trading volume. Accordingly, the results can be read more intuitively as the correlations
between informational efficiency and volatility, and efficiency and volume. No suchtransformation is required to interpret the remaining correlations as being between efficiency
and liquidity. The first two columns of Tables 3.1 and 3.2 refer to correlations between thevariables over global trading hours (TI1 to TI9). These correlations are calculated over 1152
time interval observations. The subsequent three pairs of columns to the right reflect theTokyo day session (TI1 to TI3), the London day session (TI4 to TI6) and the New York day
session (TI7 to TI9), which are calculated over 384 time intervals. Correlations in bold are
significant at the 10 percent level or less.

All global trading hours correlations for the Tokyo exchange are negative in both theplatinum and gold markets, and all except the correlation between efficiency and volume forgold are significant. This suggests that over global trading hours, the gold and platinum
markets on TOCOM are dominated by liquidity traders. New York platinum and gold market
correlations for global trading hours provide evidence for both informed and liquidity trading.
Efficiency is negatively correlated with volatility, suggesting the transactions of liquidity
traders give rise to volatility. However, efficiency is positively correlated with volume, as
hypothesised under the Admati and Pfleiderer’s (1988) asymmetric information view where
informed traders prefer to trade during periods where they will have low market impact. The
correlations between efficiency and the two liquidity measures are not significant.

We find a more nuanced view of the intraday relationships between efficiency and volatility,
volume and liquidity in the correlations for the Tokyo, London and New York day sessions.
Consistent with anecdotal evidence from market participants that firms with large physicalplatinum exposures enter the market during the Tokyo morning to hedge via TOCOM, thecorrelations for both the Tokyo and New York platinum markets support liquidity trader
interpretations during the Tokyo day. Efficiency is significantly negatively correlated withvolatility, volume and the two liquidity measures for platinum traded on TOCOM. Similarly,
all correlations are negative for platinum traded in New York during the Tokyo day. All
except the correlation between efficiency and liquidity (spread) are significant. Efficiency is
16also negatively and significantly correlated with volatility for gold in both Tokyo and New
York, with volume in New York only, and with ILLIQ in Tokyo only. While there is support
for liquidity trading in both metals during the Tokyo day, the evidence for platinum isstronger than that for gold.

During the London day session, the correlations are less definitive. The correlation between
efficiency and liquidity (ILLIQ) supports a noise trader view for the TOCOM platinum
market. However, in the New York platinum market the correlations with volume andliquidity (ILLIQ) are both positive and significant, supporting the asymmetric information
view and the transactions cost view, respectively. The the correlation with volatility is
negative and significant, suggesting liquidity trading. For the gold markets, negative
correlations between efficiency and liquidity (ILLIQ) in Tokyo, and efficiency and volatility
in New York, provide some support for liquidity trading during the London day session.

Our results for the New York day session support the dominance of informed trading for both
metals traded on both exchanges. The evidence is stronger for gold than platinum in terms of
the size of the correlations for both trade in Tokyo and New York, and in terms of the numberof significant correlations for Tokyo. Correlations between efficiency and volatility are
positive and significant over all four markets, and those between efficiency and volume arepositive and significant for platinum and gold in New York, and gold but not platinum inTokyo. These correlations suggest that liquidity traders are likely absent from the Tokyo
market during the Tokyo night session when volume and liquidity are low. This concurs withanecdotal evidence that large hedgers of physical platinum enter the market primarily during
the Tokyo morning. Informed traders appear to trade in Tokyo at night while overlappingwith the New York day, despite the relatively low liquidity compared with the Tokyo day
session. They are likely arbitraging between the two markets during the New York day.

The evidence from the correlation analysis is consistent with the patterns evident in the chartsof the regression estimates. Relatively high variance ratio (Figure 2.1) and realised volatility(Figure 2.2) model estimates occur in TI1 and TI4. This implies informational efficiency isnegatively related to volatility, implying that volatility is the result of the market transactionsof liquidity traders. From around the New York open (TI7) low variance ratio model
estimates are associated with high realised volatility estimates, consistent with the rational
adjustment of prices to new information. Taken together, Figures 2.1 and 2.3 suggest
17efficiency is negatively related to trading volume during the Tokyo day, particularly for
platinum on TOCOM. TI1 is the busiest trading time for platinum on TOCOM, and also theleast efficient time. By the New York day session, the regression model estimates suggest apositive relationship between efficiency and volume for both metals on both exchanges. The
spread model estimates (Figure 2.4) do not show a great deal of intraday variation, andaccordingly their relationship with efficiency is less clear than for the preceding variables.
However, it would appear that efficiency and liquidity are negatively related, at least for
platinum and gold on TOCOM over global trading hours, suggesting liquidity is a proxy for
uninformed trading. Similarly, the variance ratio and ILLIQ (Figure 2.5) estimates broadly
suggest a negative relationship between efficiency and liquidity in the Tokyo markets and apositive relationship in New York over global trading hours.

5. Conclusion
This paper examines the intraday seasonality of informational efficiency, return volatility,
trading volume and market liquidity in the platinum and gold futures markets on exchanges
in Tokyo and New York using high frequency 1-minute data covering global trading hours
from September 2014 to March 2015. Platinum and gold provide an interesting comparisonas Tokyo is an internationally important centre for platinum trading but not for gold. We also
examine the relationships between market microstructure characteristics to determine
whether trading in these markets is predominantly informed or liquidity driven. The article
aims to contribute to the understanding of commodity futures market microstructure, on
which there has been little research to date.

We find the following regularities in intraday market characteristics. Informational
inefficiency in both the platinum and gold markets conforms to a W-shape over global
trading hours. The Tokyo and London open, and later in the New York day, show the highest
levels of inefficiency. Day sessions in Tokyo and London start relatively inefficient andbecome more efficient. In the New York day session, the markets start relatively efficient andbecome inefficient by late in its session. Volatility also follows a similar pattern for both
metals and exchanges. It is relatively high at the open of the Tokyo, London and New Yorkday sessions, being L-shaped in Tokyo hours, U-shaped in London hours, and declining
approximately linearly in New York hours. In contrast, intraday volume and liquidity patterns
differ between the metals and/or exchanges. Trading volume in platinum is concentrated oneach of the Tokyo and New York exchanges during their day sessions, while comparatively
18

more platinum volume on TOCOM occurs through the New York day than NYMEX volume
through the Tokyo day. Tokyo platinum volume shows reasonably clear reverse-J and Lshaped patterns during the Tokyo and London day sessions, respectively. Volume in all themarkets declines monotonically during the New York day session. In the gold market,
volume builds to a peak at the New York open on COMEX that dwarfs the volume on
TOCOM. Liquidity on each exchange is greatest during that exchange's day session, andAmihud's ILLIQ shows Tokyo liquidity deteriorating over global trading hours.

Relationships uncovered between informational efficiency and volatility, volume andliquidity suggest that over global trading hours both the platinum and gold markets in Tokyo
are dominated by liquidity trading, while there is evidence supporting both liquidity andinformed trading in New York. During the Tokyo day session, liquidity traders dominate theplatinum and gold markets in both Tokyo and New York. Conversely, during the New Yorkday session, informed traders dominate.

Arbitrage means the intraday patterns of return related market characteristics, such as
efficiency and volatility, remain closely related across exchanges trading the samecommodity. However, market activity measures such as volume and liquidity can differ
substantially between the exchanges over the course of global trading hours. The Tokyo and
New York exchanges examined in this research have overlapping trading sessions. Nightsessions supplement the exchanges' daytime trading hours. This overlap of trading influences
intraday microstructure patterns on each exchange over global trading hours, and the absenceof an overlap between day trading sessions at the end of global trading hours also influences
microstructure patterns. The resulting intraday patterns share similarities with the intraday
patterns seen in the continuously traded foreign exchange markets, as identified by Ito andHashimoto (2006). Market participants in different time zones and different geographicallocations have different motivations for trading. Liquidity trading is prevalent during theTokyo day session when most volume goes through Tokyo markets. While during New York
hours, informed trading dominates during the New York exchanges' busiest times. Thisevidence suggests that futures markets for the same underlying commodity on different
exchanges have different microstructure characteristics, while both informed and liquidity
traders choose when to trade depending on market characteristics in different time zones.

19

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22

Figures

Figure 1: Monthly Contract Volume

Figure 2.1: Variance Ratio

Figure 2.2: Realised Volatility

23

Figure 2.3: Trading Volume

Figure 2.4: Spread

Figure 2.5: Illiquidity24

Tables

Table 1: Time Intervals
TimeInterval

Duration(minutes)

SessionDescribed As

TI1
TI2
TI3
TI4
TI5
TI6
TI7
TI8
TI9

125
125
125
115
115
115
115
115
115

Tokyo Day
Tokyo Day
Tokyo Day
London Day
London Day
London Day
New York Day
New York Day
New York Day

Tokyo (JST)London (GMT)

London (DST)(London Summer)

New York (EST)New York (DST)(New York Summer)

Start Time

End Time

Start Time

End Time

Start Time

End Time

Start Time

End Time

Start Time

End Time

09:00:00
11:05:00
13:10:00
16:30:00
18:25:00
20:20:00
22:15:00+00:10:00+02:05:00

11:04:59
13:09:29
15:14:59
18:24:59
20:19:59
22:14:59+00:09:59+02:04:59+03:59:59

0:00:00
02:05:00
04:10:00
07:30:00
09:25:00
11:20:00
13:15:00
15:10:00
17:05:00

02:04:59
04:09:59
06:14:59
09:24:59
11:19:59
13:14:59
15:09:59
17:04:59
18:59:59

01:00:00
03:05:00
05:10:00
08:30:00
10:25:00
12:20:00
14:15:00
16:10:00
18:05:00

03:04:59
05:09:59
07:14:59
10:24:59
12:19:59
14:14:59
16:09:59
18:04:59
19:59:59-19:00:00-21:05:00-23:10:00
02:30:00
04:25:00
06:20:00
08:15:00
10:10:00
12:05:00-21:04:59-23:09:59
01:14:59
04:24:59
06:19:59
08:14:59
10:09:59
12:04:59
13:59:59-20:00:00-22:05:00
00:10:00
03:30:00
05:25:00
07:20:00
09:15:00
11:10:00
13:05:00-22:04:59
00:09:59
02:14:59
05:24:59
07:19:59
09:14:59
11:09:59
13:04:59
14:59:59

25

Table 2.1: Summary Statistics for Platinum
Statistic
MeanMedianMinimum
MaximumStandard
Deviation
Skewness
Kurtosis
Observations

Variance
Ratio
TY
0.252
0.239
0.000
0.965

Variance
Ratio
NY
0.234
0.209
0.000
0.932

Realised
Volatility
TY
0.983
0.872
0.245
9.823

Realised
Volatility
NY
1.096
0.976
0.233
9.152

Trading
VolumeTY
14.22310.4000.287
131.040

Trading
VolumeNY
10.1276.625
0.528
60.278

0.170

0.165

0.628

0.656

13.082

0.644
0.159
1152

0.842
0.567
1152

6.412
73.1001152

4.685
44.1661152

SpreadTY

SpreadNY

Illiquidity
TY

Illiquidity
NY

1.841
1.875
1.077
3.447

1.854
1.802
0.900
3.890

19.142
12.6130.858
180.336

10.6548.603
0.833
52.357

9.471

0.261

0.416

20.105

7.855

2.939
13.860
1152

1.741
3.469
1152

0.109
3.208
1152

0.729
0.830
1152

2.914
12.853
1152

1.255
1.725
1152

SpreadTY

SpreadNY

Illiquidity
TY

Illiquidity
NY

1.277
1.268
1.082
1.755

0.539
0.532
0.442
1.286

4.958
3.377
0.544
63.842

0.843
0.366
0.074
56.556

Table 2.2: Summary Statistics for Gold
Statistic
MeanMedianMinimum
MaximumStandard
Deviation
Skewness
Kurtosis
Observations

Variance
Ratio
TY
0.270
0.256
0.000
0.879

Variance
Ratio
NY
0.225
0.193
0.000
0.907

Realised
Volatility
TY
0.845
0.716
0.229
12.630Realised
Volatility
NY
0.924
0.781
0.192
11.587

Trading
VolumeTY
34.45626.7561.826
219.360

Trading
VolumeNY
125.895
81.2390.328
807.609

0.177

0.169

0.613

0.652

27.120121.566

0.086

0.076

5.587

3.901

0.568
-0.152
1152

1.042
0.960
1152

9.136
146.0101152

5.913
72.775
1152

2.190
7.169
1152

2.024
5.044
1152

1.200
3.590
1152

4.170
29.2491152

4.231
26.0061152

8.833
10.3941152

26

Table 3.1: Correlations between Efficiency and Volume, Volatility and Liquidity for Platinum
Correlation of Efficiency with
Volatility (Realised Volatility)
Volume (Trading Volume)
Liquidity (Spread)
Liquidity (Illiquidity)

All Sessions (Global Trading Hours)
Tokyo
New York-0.151 ***-0.219 ***-0.144 ***0.098 ***
-0.019-0.127 ***0.031-0.087 ***Tokyo Day Session
Tokyo
New York-0.370 ***-0.486 ***-0.223 ***-0.174 ***-0.029-0.120 **-0.144 ***-0.187 ***London Day Session
Tokyo
New York-0.004-0.087 *0.007
0.100 **
-0.056-0.030-0.129 **0.090 *New York Day Session
Tokyo
New York
0.113 **
0.091 *
0.059
0.099 *
-0.013-0.0470.022
0.081

Note: ***, **, and * denote significance of the Pearson correlation coefficient at the 1, 5 and 10 percent levels, respectively.

Table 3.2: Correlations between Efficiency and Volume, Volatility and Liquidity for Gold
Correlation of Efficiency with
Volatility (Realised Volatility)
Volume (Trading Volume)
Liquidity (Spread)
Liquidity (Illiquidity)

All Sessions (Global Trading Hours)
Tokyo
New York-0.104 ***-0.222 ***-0.0410.150 ***
0.026
-0.123 ***0.037-0.116 ***Tokyo Day Session
Tokyo
New York-0.302 ***-0.503 ***-0.069-0.133 ***
0.062
0.065
0.059
-0.108 **Note: ***, **, and * denote significance of the Pearson correlation coefficient at the 1, 5 and 10 percent levels, respectively.

27

London Day Session
Tokyo
New York-0.078-0.170 ***
0.019
0.028
-0.012-0.031-0.024-0.115 **New York Day Session
Tokyo
New York
0.209 ***
0.156 ***
0.118 **
0.163 ***
-0.051-0.0160.013-0.009Appendix

Table A1.1: Estimates for Platinum
Variable

Constant

TI2

TI3

TI4

TI5

TI6

TI7

TI8

TI9

Variance Ratio TY
Variance Ratio NY
Realised Volatility TY
Realised Volatility NY
Trading Volume TY
Trading Volume NY
Spread TY
Spread NY
Illiquidity TY
Illiquidity NY

0.357 ***
0.352 ***
1.430 ***
1.499 ***
35.717 ***5.558 ***
1.540 ***
1.874 ***
4.647 ***
14.749 ***-0.122 ***-0.141 ***-0.796 ***-0.837 ***-23.321 ***-2.818 ***0.097 ***
0.067
3.766 **
3.627 ***

-0.111 ***-0.143 ***-0.761 ***-0.808 ***-16.639 ***-2.144 **0.089 ***
-0.004
1.106
1.529 **

-0.084 ***-0.072 ***-0.313 ***-0.263 ***-20.457 ***2.300 ***
0.309 ***
-0.0307.560 ***
-3.323 ***-0.106 ***-0.136 ***-0.626 ***-0.591 ***-26.708 ***1.067
0.369 ***
0.064
15.287 ***-3.944 ***-0.150 ***-0.155 ***-0.471 ***-0.354 ***-26.488 ***6.199 ***
0.399 ***
0.096 *
18.280 ***-5.746 ***-0.145 ***-0.171 ***-0.206 ***-0.002-22.494 ***17.579 ***0.467 ***
-0.086 *14.129 ***-11.411 ***-0.110 ***-0.123 ***-0.310 ***-0.230 ***-25.967 ***14.574 ***0.428 ***
-0.207 ***23.996 ***-11.087 ***-0.118 ***-0.121 ***-0.519 ***-0.537 ***-31.370 ***4.360 ***
0.557 ***
-0.07446.335 ***-6.501 ***Adjusted
R2
0.053
0.083
0.151
0.196
0.425
0.505
0.489
0.039
0.456
0.391

Note: ***, **, and * denote significance of the Pearson correlation coefficient at the 1, 5 and 10 percent levels, respectively.

Table A1.2: Estimates for Gold
Variable

Constant

TI2

TI3

TI4

TI5

TI6

TI7

TI8

TI9

Variance Ratio TY
Variance Ratio NY
Realised Volatility TY
Realised Volatility NY
Trading Volume TY
Trading Volume NY
Spread TY
Spread NY
Illiquidity TY
Illiquidity NY

0.397 ***
0.381 ***
1.142 ***
1.210 ***
63.094 ***50.712 ***1.207 ***
0.550 ***
1.529 ***
1.513 ***

-0.111 ***-0.188 ***-0.590 ***-0.707 ***-33.170 ***-13.753
0.018 **
-0.018 *0.989 *
-0.298-0.115 ***-0.160 ***-0.568 ***-0.660 ***-24.951 ***-9.2320.010-0.0090.429-0.294-0.075 ***-0.092 ***-0.267 ***-0.247 ***-30.503 ***39.694 ***0.069 ***
0.000
2.429 ***
-0.471-0.164 ***-0.186 ***-0.433 ***-0.447 ***-39.068 ***35.948 ***0.071 ***
0.005
3.488 ***
-0.361-0.178 ***-0.205 ***-0.241 ***-0.152 **-29.068 ***107.688 ***0.084 ***
0.002
3.305 ***
-0.838 *-0.174 ***-0.205 ***-0.0180.162 **
-15.764 ***264.237 ***0.099 ***
-0.016 *2.421 ***
-1.256 ***-0.170 ***-0.195 ***-0.173 **-0.127 *-34.962 ***166.044 ***0.085 ***
-0.028 ***5.219 ***
-1.316 ***-0.156 ***-0.175 ***-0.389 ***-0.391 ***-50.256 ***86.021 ***0.195 ***
-0.028 ***12.584 ***-1.196 **Note: ***, **, and * denote significance of the Pearson correlation coefficient at the 1, 5 and 10 percent levels, respectively.

28

Adjusted
R2
0.093
0.139
0.104
0.172
0.243
0.513
0.421
0.019
0.408
0.007