101808

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httpslidepdfcomreaderfull101808 111

Research ArticleGenerating Moving Average Trading Rules on the Oil FuturesMarket with Genetic Algorithms

Lijun Wang12 Haizhong An123 Xiaohua Xia4 Xiaojia Liu12

Xiaoqi Sun12 and Xuan Huang 12

983089 School of Humanities and Economic Management China University of Geosciences Beijing 983089983088983088983088983096983091 China983090 Key Laboratory of Carrying Capacity Assessment for Resource and Environment Ministry of Land and Resources

Beijing 983089983088983088983088983096983091 China983091 Lab of Resources and Environmental Management China University of Geosciences Beijing 983089983088983088983088983096983091 China983092 Institute of Chinarsquos Economic Reform and Development Renmin University of China Beijing 983089983088983088983096983095983090 China

Correspondence should be addressed to Haizhong An ahz983091983094983097983089983094983091com

Received 983089983097 February 983090983088983089983092 Revised 983092 May 983090983088983089983092 Accepted 983095 May 983090983088983089983092 Published 983090983094 May 983090983088983089983092

Academic Editor Wei Chen

Copyright copy 983090983088983089983092 Lijun Wang et al Tis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Te crude oil utures market plays a critical role in energy 1047297nance o gain greater investment return scholars and traders usetechnical indicators when selecting trading strategies in oil utures market In this paper the authors used moving average prices o

oil utures with genetic algorithms to generatepro1047297table trading rules We de1047297ned individuals with different combinationso periodlengths and calculation methods as moving average trading rules and used genetic algorithms to search or the suitable lengths o moving average periods and the appropriate calculation methods Te authors used daily crude oil prices o NYMEX utures rom983089983097983096983091 to 983090983088983089983091 to evaluate and select moving average rules We compared the generated trading rules with the buy-and-hold (BH)strategy to determine whether generated moving average trading rules can obtain excess returns in the crude oil utures marketTrough 983092983090983088 experiments we determine that the generated trading rules help traders make pro1047297ts when there are obvious price1047298uctuations Generated trading rules can realize excess returns when price alls and experiences signi1047297cant 1047298uctuations while BHstrategy is better when price increases or is smooth with ew 1047298uctuations Te results can help traders choose better strategies indifferent circumstances

1 Introduction

Energy is vital or economic development Household activ-ities industrial production and inrastructure investmentsall consume energy directly or indirectly no matter indeveloping or developed countries [983089] Issues pertaining toenergy trade [983090] energy efficiency [983091] energy policy [983092ndash983094] energy consumption [983095] and energy 1047297nance [983096] havereceived more importance in recent years Crude oil uturesmarket is a crucial part o energy 1047297nance within the scopeo the global energy market raders and researchers employ technical analysis tools to identiy gainul trading rules in1047297nancial markets Accordingly moving average indicatorsare commonly used in technical analysis to actualize greaterreturns Tis paper attempts to answer whether in real lie

an investor can use moving average technical trading rules toobtain excess returns through searching or pro1047297tablemoving

average trading rules with genetic algorithms in the crude oilutures market

Genetic algorithms are widely used in social sciences[983097 983089983088] especially in certain complex issues where it is difficultto conduct precise calculations It is a trend to apply physicalor mathematical methods in energy and resource economics[983089983089ndash983089983094] Researchers have applied genetic algorithms to theprediction o coal production-environmental pollution [983089983095]the internal selection and market selection behavior in themarket [983089983096] the crude oil demand orecast [983089983097] the mini-mization o uel costs andgaseous emissionso electric powergeneration [983090983088] and the Forex trading system [983090983089] Withrespect to the 1047297nancial technical analysis issues scholars use

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014 Article ID 101808 10 pageshttpdxdoiorg1011552014101808

7262019 101808


983090 Mathematical Problems in Engineering

genetic algorithms to search best trading rules and pro1047297tabletechnical indicators when making investment decisions [983090983090ndash983090983093] Genetic algorithms are combined with other tools suchas the agent-based model [983090983094] uzzy math theory [983090983095] andneural networks [983090983096] Tere are also some studies that haveused genetic algorithms to orecast the price trends in the

1047297nancial market [983090983097 983091983088] or the exchange rate o the oreignexchange market [983091983089] As there are a vast number o technicaltrading rules and technical indicators available in the crudeoil utures market it is impractical to use ergodic calculationsor certain other accurate calculation methods Tereoreusing genetic algorithms is a easible way to resolve this issue

Moving average indicators have been widely used instudies o stocks and utures markets [983091983090ndash983091983095] wo movingaverages o different lengths are compared to orecast theprice trends in different markets Short moving averagesare more sensitive to price changes than long ones I ashort moving average price is higher than a long periodmoving average price traders will believe the price will riseand take long positions When the short moving averageprice alls and crosses with the long one opposite tradingactivities will be taken [983091983096] Allen and Karjalainen (AK) [983091983097]used genetic algorithms to identiy technical trading rules instock markets with daily prices o the SampP 983093983088983088 Te movingaverage price was used as one o the many indicators o thetechnical rules Other indicators such as the mean valueand maximum value are also used when making investmentdecisions Wang [983092983088] conducted similar research on spot andutures markets using genetic programing while How [983092983089]applied AKrsquos method to different cap stocks to determinethe relevance o size William comparing different technicalrules and arti1047297cial neural network (ANN) rules regarding oilutures market determined that the ANN is a good tool thuscasting doubt on the efficiency o the oil market [ 983091983096] All o these studies combine moving average indicators with otherindicators to generate trading rules However in this paperwe utilize moving averages to generate trading rules whichmay be a simple and efficient approach

Te perormance o a moving average trading rule isaffected signi1047297cantly by the period lengths [983092983090] Tereore1047297nding optimal lengths o the two periods above is a centralissue in technical analysis literature A variety o lengthshave been tried in existing research projects [983092983091ndash983092983096] In theexisting research most o moving average rules use 1047297xedmoving average period lengths and single moving averagecalculation method However it is better to use variable

lengths or different investment periods [983092983097 983093983088] and there aredifferenttypes o moving average calculation method that canbe used in technical analysis

In this paper considering that the optimal length o themoving average periods and the best calculation method may

vary rom one occasion to another we use genetic algorithmsto determine the suitable length o the moving average periodand the appropriate method Six moving average calculationmethods are considered in this paper and genetic algorithmscan help us 1047297nd out the best method and appropriate periodlengths or different circumstances Accordingly we are ableto present the most suitable moving average trading rules ortraders in the crude oil utures market

2 Data and Method

983090983089 Data We use the daily prices o the crude oil uturecontract 983089 or the period 983089983097983096983091 to 983090983088983089983091 rom the New York Mercantile Exchange (Data Source httpwwweiagovdnavpetpet pri ut s983089 dhtm) We select 983090983088 groups o sam-ple data each containing 983089983088983088983088 daily prices In the 983089983088983088983088 daily prices a 983093983088983088-day price series is used to train trading rulesin every generation Te ollowing 983090983088983088 prices are used toselect the best generated trading rule rom all generationsand the last 983091983088983088 daily prices are used to determine whetherthe generated rule can acquire excess returns Te 1047297rst groupbegins in 983089983097983096983093 the last group ends in 983090983088983089983091 and each 983089983088983088983088-day price series with a step o 983091983088983088 is selected We must alsoinclude 983093983088983088 more daily prices beore each sample series tocalculate the moving pricesor the sampleperiod Tus every independent experiment requires a 983089983093983088983088-day price series Tedata we use are presented in Figure 983089

983090983090 Method Moving average trading rules acilitatedecision-making or traders by comparing two moving

averages o different periods In this way traders can predictthe price trend by analyzing the volatility o the movingaverage prices Tere are six moving average indictors usually used in technical analysis simple moving average (SMA)weighted moving average (WMA) exponential movingaverage (EMA) adaptive moving average (AMA) typicalprice moving average (PMA) and triangular movingaverage (MA) Te calculation methods o moving averageindicators are presented in able 983089

o use a moving average trading rule in the oil uturesmarket at least three parameters must be set to establish atrading strategy Tese parameters include the lengths o twomoving average periods and the choice o the moving averagemethod rom the above sixtypes Other researchers have useddifferent lengths o sample periods in their studies In thispaper we use genetic algorithms to determine appropriatelengths o the moving average period According to existingliterature the long period is generally between 983090983088 and 983090983088983088days (very ew studies use periods longer than 983090983088983088 days)[983091983096 983091983097] and the short period is generally no longer than 983094983088days

I the long average price is lower than the short averageprice a trader will take a long position It ollows thatin opposite situations opposite strategies will be adoptedNoting the price volatility in the utures market taking a

long position when the short average price exceeds the longaverage price by at least one standard deviation in the shortperiod maybe a goodrule Conversely taking a short positionmay also be a good rule Tereore we designed the two rulesin our initial trading rules Te detailed calculation methodso the six moving averages are presented in Figure 983090

A 983089983095-binary string is used to represent a trading rulein which a seven-binary substring represents (M-N) ( isthe long period length and 1038389 is the short period length)a six-binary substring is 1038389 (1038389 belongs to the range o 983089to 983094983092) a three-binary substring represents the calculationmethod o average prices In this paper the range o to 1038389 is 983093 to 983089983091983090 Te last binary determines whether to

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Mathematical Problems in Engineering 983091

983137983138983148983141 983089 Details o the six moving average indicators

Indicator Calculation method (1103925 denotes price)

SMA SMA (907317) = 1

minus1

9917611038389=0

11039251103925minus1038389

WMA WMA(907317) = summinus1

1038389=0 ( minus )11039251103925minus1038389

summinus1

1038389=0 ( minus )

EMAEMA(907317) = EMA(907317 minus 1) + SC 104861611039251103925 minus EMA (907317 minus 1)1048617

where SC = 2(1 + )

AMA

AMA(907317) = AMA(907317 minus 1) + SSC11039252 104861611039251103925 minus AMA (907317 minus 1)1048617

where SSC1103925 = ER 1103925 (astSC minus slowSC) + slowSC

astSC = 2(1 + 2)

slowSC = 2(1 + 30)

ER 1103925 =11039251103925 minus 11039251103925minus

sum1103925

1038389=1103925minus+1

11039251038389 minus 11039251038389minus1

PMA PMA(907317) = (high + low + close)

3

where high = max(1103925907317 1103925907317minus1 1103925907317minus+1) low = min(1103925907317 1103925907317minus1 1103925907317minus+1) close = 1103925907317

MA MA(907317) = 1

minus1

9917611038389=0

SAM(907317 minus )

200 days

200 days

200 days

200 days 300 days

300 days

300 days

300 days

500 days

500 days

500 days 500 days

500 days

500 days

500 days 500 days

March 29 1985April 4 1983

March 29 1985

June 11 1986

August 21 1987

March 10 2009 February 26 2013

February 26 2013

August 13 1991

June 4 1990

March 27 1989Period 1

Period 2

Period 3

Period 21

Auxiliary data calculate the moving average prices in the training period

Training data evaluate and select the generated trading rules in each generation

Selection data test the best individual in every generation identify the best trading rule in a trail

Test data test the generated moving average trading rule to actualize excess return

Periods 4 5 20

F983145983143983157983154983141 983089 Data selection

change trading strategies only when there is more than onestandard deviation difference between two moving averageprices Te structure o trading rules is presented in Figure 983090Te 1047297tness o a trading rule is calculated according to thepro1047297t it can make in the crude oil utures market o comparegenerated trading rules with the BH (buy-and-hold takingthe long position throughout the period) strategy the pro1047297to a generated rule is the excess return rate that exceeds theBH strategy

Te calculation method o the return rate reerences AKrsquosmethod Te difference is that we allow a trader to hold aposition or a long time and we do not calculate the returnevery day Consider

Ra = Ral + Ras + R minus Rbh

Ral = sum

1038389=1 10486161048616out minus in1048617 in lowast (1 minus ) (1 + )1048617Rm

Ras = sum907317


Rbh = 983080begin minus end983081

begin

lowast (1 minus ) (1 + )Rm

(983089)

Ra is the excess return rate o a long position strategythat is the sum o the return o the long position and short

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Seven-binary Six-binary ree-binary One-binary

Decimal x Decimal y Decimal z Boolean sd

1 SMA

2 WMA

3 EMA

4 AMA

5 TPMA

6 TMA

Each string represents a trading rule

Take a long position if the moving average price (using methodI)

of M -days is lower than that of N -days and take a short position in

the opposite case If thesd is 1 keep out of the market to earn the

risk free return until the difference between the two moving

averages exceeds the standard deviation of N -days prices

Method I = mod ((z + 1) 6) (1ndash6)

Short period N = y + 1 (1sim64) Long period M = N + x + 5 (6ndash196) Marker sd = 0 or 1

Binary to decimalor boolean

F983145983143983157983154983141 983090 Structure o trading rules

position R is the risk ree return when out o market andRbh is thereturn rate o the BH strategy in thesample periodRm is the margin ratio o the utures market Te parameter denotes the one-way transaction cost rate in and out

represent the opening price and closing price o a position(long or short) respectively begin is the price o the 1047297rst day in a whole period and end is the price o the last day As weignore the amount o change in the everyday margin and thedeadline o the contract a trader can maintain his strategy by taking new positions when a contract nears its closing date

Te 1047297tness value is a number between 983088 and 983090 calculatedthrough nonlinear conversion according to Ra Te 1047297tness

value calculation selection crossover and mutation o indi-

viduals are implemented using the GA toolbox o Sheffieldin the Matlab platorm In every generation to avoid theover1047297tting o training data the best trading rule in every generation will be tested in a selection sample period (the983090983088983088-day price series) Only when the 1047297tness value is higherthan the best value in the last generation or when the two

values are almost the same (last minusnow lt 983088983088983093) can the tradingrule be marked as the best thus ar In every generation 983097983088percent o the population will be selected to orm a new generation while the other 983089983088 percent will be randomly generated Accordingly the evolution o individuals usinggenetic algorithms in a single independent experiment canbe summarized as ollows

Step 983089 (initialize population) Randomly create an initialpopulation o 983090983088 moving average trading rules

Step 983090 (evaluate individuals) Te 1047297tness o every individualis calculated in the evaluation step Te program calculatesthe moving average prices in two different scales during thetraining period using the auxiliary data and determines thepositions on each trading day Te excess return rate o every individual is then calculated Finally the 1047297tness value o eachindividual is calculated according to the excess return rate

Step 983091 (remember the best trading rule) Select the rule withthe highest 1047297tness value and evaluate it or the selection

period to obtain its return rate I it is better than or notinerior to the current best rule it will be marked as the besttrading rule I its return rate is lower than or less than 983088983088983093higher than the current rate we retain the current rule as thebest one

Step 983092 (generate new population) Selecting 983089983096 individualsaccording to their 1047297tness values the same individual couldbe selected more than once Tereore randomly create 983090additional trading rules With a probability o 983088983095 perorma recombination operation to generate a new populationAccordingly all the recombination rules will be mutated witha probability o 983088983088983093

Step 983093 Return to Step 983090 and repeat 983093983088 times

Step 983094 (test the best trading rule) est the best trading rule asidenti1047297ed by the above program Tis will generate the returnrate and indicate whether genetic algorithms can help tradersactualize excess returns during this sample period

3 Results

Because in this paper we have not considered the amount o assets we assume the margin ratio to be 983088983088983093 In act as theparameter has no signi1047297cant effect on our experiment results

the return rate is increased twenty times With 983090983088 trials ineach period 983092983090983088 independent experiments are conducted todetermine useul moving average trading rules in the crudeoil utures market Te prices we used or the 983090983089 periods areshown in Figure 983091

Based on previous studies [983091983097 983092983088 983093983089] and on the decisionto select an intermediate value or this study the transactioncost rate is set at 983088983089 or the 983092983090983088 experiments Te risk reereturn rate is 983090 which is based primarily on the short-termtreasury bond rate [983092983089]

O the 983092983090983088 trials 983090983090983094 earn pro1047297ts With an average returnrate o 983089983092983092983094 it is concluded that genetic algorithms canacilitate traders to obtain returns in the crude oil utures

7262019 101808



8503 89030

20

40(1)

8606 900510

20

30(2)

8708 91070

50(3)

8810 92100

50(4)

9001 93120

50(5)

9103 950210

20

30(6)

9205 960510

20

30(7)

9308 970710

20

30(8)

9410 980910

20

30(9)

9512 991210

20

30(10)

9703 01020

20

40(11)

9805 02040

20

40(12)

9907 03070

20

40(13)

0010 04090

50

100(14)

0112 05120

50

100(15)

0303 07020

50

100(16)

0405 08050

100

200(17)

0508 09070

100

200(18)

0610 10090

100

200(19)

0712 11120

100

200(20)

0903 13020

100

200(21)

F983145983143983157983154983141 983091 Sample data

market However moving average trading rules identi1047297ed by genetic algorithms do not result in excess returns as thereare only 983096 periods in which generated trading rules resultedin traders receiving excess returns Given that the price o

crude oil utures increased many times during the sampleperiod we urthercontendthat genetic algorithms are helpulin investments

For a better understanding we divide the 983090983089 periods into983092 categories according to the results (see the last column o able 983090)

Category 983089 (periods 983090 983091 and 983097) In these periods generatedtrading rules not only help traders obtain returns but alsohelp them to realize excess returns Generated trading rulesgenerate more pro1047297ts than the BH strategy in periods 983091and 983097 In period 983090 the BH strategy loses money whilethe generated trading rules as determined by the genetic

algorithms result in pro1047297ts Tus the generated trading rulesare ar superior to the BH strategy in this period A commoneature o these three periodsin Category 983089 is that thecrude oilprices ell during the test period and experienced signi1047297cant

1047298uctuations

Category 983090 (periods 983093 983096 983089983090 983089983094 and 983089983096) Generated movingaverage trading rules ail to generate pro1047297ts during these 1047297veperiods Even so the generated rules perormed better thanthe BH strategy as they signi1047297cantly reduced losses In theseperiods prices declined smoothly experiencing some small1047298uctuations during the process

Category 983091 (periods 983089 983094 983095 983089983088 983089983089 983089983092 983089983093 and 983089983095) In theseeight sample data periods genetic algorithms help tradersto identiy suitable moving average trading rules Howeverthe traders ailed to obtain excess returns While prices

7262019 101808



983137983138983148983141 983090 Results o experiment

Period Rbh Classi1047297cation

983089 983091 983089983090 983091983095983094983096 983088983094983094983091 minus983091983089983088983093 983091

983090 983090983088 983090983088 minus983090983097983092983094 983090983096983097983097 983093983096983092983093 983089

983091 983089983093 983089983094 983093983090983097983097 983095983095983089983095 983090983092983089983097 983089

983092 983089 983094 983088983094983092983095 minus983088983096983094983090 minus983089983093983089983088 983092983093 983090983088 983089983089 minus983095983089983096983093 minus983088983088983097983095 983095983088983096983096 983090

983094 983089 983089983090 983092983097983095983094 983088983096983088983096 minus983092983089983094983096 983091

983095 983093 983089983089 983093983090983092983088 983089983096983093983092 minus983091983091983096983094 983091

983096 983089983088 983097 minus983089983089983095983093 minus983088983091983093983095 983088983096983089983096 983090

983097 983089983097 983089983090 minus983093983094983089983088 983088983094983097983089 983094983091983088983089 983089

983089983088 983088 983089983094 983089983094983091983091983096 983094983097983092983091 minus983097983091983097983094 983091

983089983089 983089 983089983091 983090983095983092983088 983088983089983090983095 minus983090983094983089983091 983091

983089983090 983089983093 983089983089 minus983089983092983090983088 minus983088983093983095983094 983088983096983092983092 983090

983089983091 983088 983095 983092983091983092983091 minus983090983090983097983094 minus983094983094983092983088 983092

983089983092 983088 983089983092 983089983092983088983094983097 983091983089983092983089 minus983089983088983097983090983096 983091

983089983093 983095 983096 983090983090983096983095 983088983090983095983091 minus983090983088983089983092 983091

983089983094 983089983090 983097 minus983088983095983089983093 minus983088983088983097983090 983088983094983090983090 983090983089983095 983088 983090983088 983090983094983090983090983095 983090983089983088983091983095 minus983093983089983097983088 983091

983089983096 983090983088 983091 minus983097983095983092983094 minus983092983089983091983089 983093983094983089983093 983090

983089983097 983088 983088 983091983093983089983090 minus983094983088983097983089 minus983097983094983088983091 983092

983090983088 983089 983089983088 983090983097983094983096 minus983088983089983097983091 minus983091983089983094983089 983092

983090983089 983095 983094 minus983088983089983094983090 minus983089983088983097983090 minus983088983097983091983088 983092

is the number o generated trading rules receiving positive excess returns compared with the BH strategy in the 983090983088 trials is the number o generatedtrading rules acquiring returns in the test periods Rbh is the return rate o the BH strategy is the average return rate o the 983090983088 trials in each period isthe average excess return rate o 983090983088 trials in each period

steadily increase in these periods there are also some minor1047298uctuations which cause the genetic algorithms to be inerior

to the BH strategy in these periods

Category 983092 (periods 983092 983089983091 983089983097 983090983088 and 983090983089) Genetic algorithmtrading rules demonstrate poor perormance in these 1047297veperiods In period 983090983089 the BH strategy yields negative returnsOur genetic trading rules yield more severe losses TeBH strategy is considered superior to the generated tradingrules in the other our periods as the BH strategy yieldssome returns While there are no signi1047297cant changes in theprices level in these periods the prices are in volatile statesthroughout the 1047297ve periods Slight price changes with noapparent trends render the generated trading rules helplessin predicting price changes and providing returns

We use genetic algorithms to search good moving averagetrading rules or traders in the crude oil market able 983091which shows the average number o and 1038389 or every period indicates that the value o long period () has aclose relationship with the volatility o the prices in thesample period A large is set in periods with signi1047297cant1047298uctuations and a small is selected or periods in whichprice is relatively stable

Te distribution o is shown in Figure 983092 Te valueo Probability is very small and does not ollow normaldistribution Te 1047297gurepresentsa typical at tail characteristicwith a kurtosis o 983090983091983094 Compared with normal distributionthere are more values located in the tails o the distribution in

our results Only in hal o the 983092983090983088 experiments is between983095983088 days and 983089983091983088 days Te values are decentralized and we

believe it is more scienti1047297c to choose the best lengths o thetwo periods using a training process that we have used in thispaper in actual investment

Among the six moving average calculation methodsAMA and MA are used more ofen than the other our(see able 983092) as more than hal o the generated movingaverage trading rules use AMA or MA A small number o generated trading rules use WMA and EMA while PMAand SMA which are easy to calculate are requently used insome periods such as periods 983089 983090 983091 983089983090 983089983097 and 983090983089

Te selection o calculation method is associated with theprice trends and volatility Figure 983093 shows that PMA is used983091983089 times in the 983094983088 independent experiments in periods 983090 983091

and 983097 (Category 983089) Different rom the overall proportionPMA is the most popular calculation method when pricealls during the period and experienced signi1047297cant 1047298uctua-tions AMA is the most popular method in the other threecategories EMA is never used in Categories 983089 and983092 Howeverit takes a 983090983092 proportion in Category 983090 more than MASMA PMA and WMA Te proportions o MA andSMA have no signi1047297cant differences in different categoriesIn category 983092 prices change with no apparent trends No onemethod has obvious advantage over the others

Te results o 983090983088 experiments in the same period indicatehigh consistency on the value sd (able 983093) When prices1047298uctuate such as in periods 983089 983090 983095 983096 983089983091 983089983097 and 983090983088 then not

7262019 101808



983137983138983148983141 983091 Te average value o and 1038389 in each period

Period 983089 983090 983091 983092 983093 983094 983095 983096 983097 983089983088 983089983089 983089983090 983089983091 983089983092 983089983093 983089983094 983089983095 983089983096 983089983097 983090983088 983090983089 Avg

Avg () 983089983088983092 983089983088983096 983094983093 983089983090983089 983089983088983089 983093983097 983093983089 983093983093 983089983092983091 983089983088983095 983089983092983088 983089983091983089 983089983089983096 983096983089 983095983096 983097983094 983089983094983088 983089983089983097 983089983089983090 983089983088983089 983095983089 983089983088983089

Avg (1038389) 983090983092 983091983094 983089983093 983092983093 983090983097 983090983097 983090983094 983089983094 983092983095 983091983095 983091983094 983092983091 983092983092 983092983095 983090983090 983089983096 983093983091 983090983092 983089983097 983091983089 983092983088 983091983090

983137983138983148983141 983092 Calculation methods o moving average price in each period

Method Period

983089 983090 983091 983092 983093 983094 983095 983096 983097 983089983088 983089983089 983089983090 983089983091 983089983092 983089983093 983089983094 983089983095 983089983096 983089983097 983090983088 983090983089 Count

SMA 983095 983092 983089 983092 983091 983091 983095 983092 983089983088 983089 983090 983089 983089983091 983094 983091 983094983097

WMA 983089 983089 983089 983093 983091 983090 983089 983091 983094 983090983091

EMA 983089 983092 983095 983090 983090 983089983093 983091983089

AMA 983089 983089 983090983088 983089983093 983089983092 983096 983096 983090 983097 983092 983089983096 983089983094 983089983096 983090 983089 983096 983089983092983093

PMA 983096 983089983097 983089983090 983090 983091 983090 983094 983090 983089 983091 983097 983094983095

MA 983090 983092 983091 983089 983096 983089983089 983089983089 983090 983089983091 983090 983089983097 983089 983089 983095 983096983093

opening positions until one average price exceeds another by

at least one standard deviation is the best option When theprice is relatively stable an investment decision should bemade immediately as long as the two moving averages cross

4 Discussion

Tis paper attempts to generate moving average tradingrules in the oil utures market using genetic algorithmsDifferent rom other studies we use only moving averages astechnical indicators to identiy useul moving average tradingrules without any other complex technical analysis tools orindicators Moving average trading rules are easy or tradersto operate and they are straightorward regardless o thesituation o identiy the best trading rules in the crude oilutures market we use genetic algorithms to select all theparameters in the moving average trading rules dynamically rather than doing so in a 1047297xed manner

According to our genetic calculations using geneticalgorithms to 1047297nd out the best lengths o the two movingaverage periods is advocated because the generated lengthsdiffer rom each other in different price trends Static movingaverage trading rules with 1047297xed period lengths cannot adaptto complex 1047298uctuations o price in different periods Atraining process however which takes dynamic eatures o price1047298uctuations intoconsiderationcan helptraders 1047297nd outthe optimal lengths o the two moving periods o a trading

ruleAmong the six moving average methods the AMA and

MAare the most popular among the generated trading rulesas these two methods have the ability to adapt to the pricetrends Te AMA can change the weights o the current priceaccording to the volatility in the last several days As theMA is the average o the SMA it more accurately re1047298ectsthe price level However the selection o best moving averagecalculation method is affected by price trends raders canchoose methods more scienti1047297cally according to the pricetrends and 1047298uctuations Based on our experiment resultsPMA is an optimal choice when price experiences a declineprocess with signi1047297cant 1047298uctuations and generating moving

average trading rules are outstanding compared with BH

strategy in these occasions Although EMA takes a very small proportion in the total 983092983090983088 experiments it is alsoan applicable method other than AMA when price allssmoothly

For the periods in which the price volatility is apparentdecisions will not be made until the difference betweenthe two averages exceeds the standard deviation o theshort sample prices thereby reducing the transaction riskHowever this method is not suitable or a period in whichthe price is relatively stable In these situationshesitation may sometimes cause traders to miss possible pro1047297t opportunities

As a whole generated moving average trading rules canhelp traders make pro1047297ts in the long term However genetic

algorithms cannot guarantee access to additional revenuein every period as they are only useul in acquiring excessreturns in special situations Te generated moving averagetrading rules demonstrate outstanding perormance whenthe crude oil utures price alls with signi1047297cant 1047298uctuationsTe BH strategy will lose on these occasions while thegenerated trading rule can help traders oresee a decline inprice and reduce losses Our trading rules also yield positivereturns during the 1047298uctuations by the timely changing o positions

When the price alls smoothly with ew 1047298uctuations inthe process generated trading rules can yield excess returnscompared to the BH strategy Although genetic algorithms

cannot help traders receive positive returns during theseperiods the algorithms can help traders reduce loss by changing positions with the change o price trends Whenthe price is stable or rising smoothly the generated rulesmay generate returns However they cannot generate morereturns than the BH strategy Limited returns cannot affordthe transaction costsWhen the price alls thegenerated rulesmay be superior to the BH strategy Genetic algorithms canalso help traders make pro1047297ts in the process o price increaseswith small 1047298uctuations In these periods the BH strategy isbetter than generated trading rules because the transactionsin the process generate transaction costs and may miss somepro1047297t opportunities Generated moving average trading rules

7262019 101808



983137983138983148983141 983093 Numbers o trading rules in which sd = 983089

Period 983089 983090 983091 983092 983093 983094 983095 983096 983097 983089983088 983089983089 983089983090 983089983091 983089983092 983089983093 983089983094 983089983095 983089983096 983089983097 983090983088 983090983089 Count

Count 983089983097 983089983097 983090983088 983088 983093 983091 983089983091 983089983090 983088 983090 983088 983088 983089983091 983090 983088 983090 983088 983089 983090983088 983089983097 983088 983089983093983088

0

4

8

12

16

20

24

28

32

20 40 60 80 100 120 140 160 180

Mean 1009833

Median 1020000

Maximum 1940000

Minimum 6000000

Std dev 4443764

Skewness 0011466

Kurtosis 2361692

Jarque-Bera 7139346

Probability 0028165

Series MSample 1 420

Observations 420

F983145983143983157983154983141 983092 Distribution o

0 02 04 06 08 1

C a t e g o r y 1

C a t e g o r y 2

C a t e g o r y 3

C a t e g o r y 4

SMA

WMA

EMA

AMA

TPMA

TMA

F983145983143983157983154983141 983093 Proportions o methods in different categories

have poor perormance i there are no notable trends in theprice change In these periods moving average indicatorscannot 1047297nd pro1047297t opportunities because the volatility is toosmall Te trends o price changes are delayed by the movingaverage method Tereore when a decision is made the pricetrend must also change and as a result there is no doubt thatthe trader will experience de1047297cits

Using genetic algorithms moving average trading rulesdo help traders to gain returns in the actual utures market

We also identi1047297ed the best lengths or the two periods withrespect to moving average rules and recommend the movingaverage calculation method or the crude oil utures marketechnical trading rules with only moving average indicatorsgenerated by genetic algorithms demonstrate no sufficientadvantages compared to the BH strategy because the overallprice increased during the 983091983088-year period Nevertheless gen-erated moving trading rules are bene1047297cial or traders under

certain circumstances especially when there are signi1047297cantchanges in pricesIn this paper we search best trading rules according to the

return rate o each one without regard to asset conditions andopen interest which proves to be the greatest limitation o thestudy o improve the accuracy o the results a simulationwith actual assets is recommended Accordingly we willundertake this endeavor in a subsequent research

5 Concluding Remarks

We conclude that the genetic algorithms identiy bettertechnical rules that allow traders to actualize pro1047297ts rom

their investments While we have no evidence to demonstratethat generated trading rules result in greater returns thandoes the BH strategy our conclusion is consistent with theefficient market hypothesis While generated trading rulesacilitate traders in realizing excess returns with respect totheir investing activities under speci1047297c circumstances they cannot at least by using moving average trading rules ensuremore long-term excess returns than the BH strategy Withrespect to the selection o two periods 1047297nding out optimallengths using genetic algorithms is helpul or making morepro1047297ts O the six moving average indicators AMA and MAare the most popular moving average calculation methodsor the crude oil utures market in total while PMA is an

7262019 101808



outstanding method in some occasion When the crude oilprices demonstrate notable volatility a trader is advised towait until the difference o the two moving averages exceedsthe standard deviation o the short period and vice versa

Basedon the above analysis it is better to use BH strategy when the price increases or is stable However generated

moving average trading rules are better than BH strategy when crude oil utures price decreases With respect to themoving average calculation method it is advocated to usePMA when price alls with signi1047297cant 1047298uctuations andAMA when price alls smoothly although PMA is not apopular method overall We propose variable moving averagetrading rules generated by training processes rather thanstatic moving average trading rules in the crude oil uturesmarkets

Conflict of Interests

Te authors declare that there is no con1047298ict o interests

regarding the publication o this paper

Authorsrsquo Contribution

Model design was done by Haizhong An Lijun Wangand Xuan Huang program development and experimentsperormance were done by Xiaojia Liu and Lijun Wang dataanalysis was done by Haizhong An Xiaohua Xia and XiaoqiSun paper composition was done by Lijun Wang XiaohuaXia and Xiaojia Liu and literature retrieval and manuscriptediting were done by Xiaojia Liu Xuan Huang and XiaoqiSun

Acknowledgments

Tis research was partly supported by the NSFC (China)(Grant no 983095983089983089983095983091983089983097983097) and Humanities and the Social Sciencesplanning unds project under the Ministry o Education o the PRC (Grant no 983089983088YJA983094983091983088983088983088983089) Te authors would like toacknowledge valuable suggestions rom Wei Fang XiaoliangJia and Qier An

References

[983089] Z M Chen and G Q Chen ldquoDemand-driven energy require-ment o world economy 983090983088983088983095 a multi-region input-output

network simulationrdquo Communications in Nonlinear Science and Numerical Simulation vol 983089983096 no 983095 pp 983089983095983093983095ndash983089983095983095983092 983090983088983089983091

[983090] G Wu L-C Liu and Y-M Wei ldquoComparison o Chinarsquos oilimport risk results based on portolio theory and a diversi1047297ca-tion index approachrdquo Energy Policy vol 983091983095 no 983097pp 983091983093983093983095ndash983091983093983094983093983090983088983088983097

[983091] X H Xia G Huang G Q Chen B Zhang Z M Chenand Q Yang ldquoEnergy security efficiency and carbon emissiono Chinese industryrdquo Energy Policy vol 983091983097 no 983094 pp 983091983093983090983088ndash983091983093983090983096983090983088983089983089

[983092] X H Xia and G Q Chen ldquoEnergy abatement in Chineseindustry cost evaluation o regulation strategies and allocationalternativesrdquo Energy Policy vol 983092983093 pp 983092983092983097ndash983092983093983096 983090983088983089983090

[983093] N Cui Y Lei and W Fang ldquoDesign and impact estimation o areorm program o Chinarsquos tax and ee policies or low-grade oiland gas resourcesrdquo Petroleum Science vol 983096 no 983092 pp 983093983089983093ndash983093983090983094983090983088983089983089

[983094] Y L Lei N Cui and D Y Pan ldquoEconomic and socialeffects analysis o mineral development in China and policy implicationsrdquo Resources Policy vol 983091983096 pp 983092983092983096ndash983092983093983095 983090983088983089983091

[983095] Z M Chen and G Q Chen ldquoAn overview o energy consump-tion o the globalized world economyrdquo Energy Policy vol 983091983097 no983089983088 pp 983093983097983090983088ndash983093983097983090983096 983090983088983089983089

[983096] N Nomikos and K Andriosopoulos ldquoModelling energy spotprices empirical evidence rom NYMEXrdquo Energy Economics vol 983091983092 no 983092 pp 983089983089983093983091ndash983089983089983094983097 983090983088983089983090

[983097] G B Ning Z J Zhen P Wang Y Li and H X Yin ldquoEconomicanalysison value chain o taxi 1047298eet with battery-swappingmodeusing multiobjectivegenetic algorithmrdquo Mathematical Problemsin Engineering vol 983090983088983089983090 Article ID 983089983095983093983097983089983090 983089983093 pages 983090983088983089983090

[983089983088] S Chai Y B Li J Wang and C Wu ldquoA genetic algorithmor task scheduling on NoC using FDH cross efficiencyrdquo Mathematical Problems in Engineering vol 983090983088983089983091 Article ID

983095983088983096983092983097983093 983089983094 pages 983090983088983089983091[983089983089] G Q Chen and B Chen ldquoResource analysis o the Chinese

society 983089983097983096983088ndash983090983088983088983090basedon exergy Part 983089 ossiluelsand energy mineralsrdquo Energy Policy vol 983091983093 no 983092 pp 983090983088983091983096ndash983090983088983093983088 983090983088983088983095

[983089983090] Z Chen G Chen X Xia and S Xu ldquoGlobal network o embodied water 1047298ow by systems input-output simulationrdquoFrontiers of Earth Science vol 983094 no 983091 pp 983091983091983089ndash983091983092983092 983090983088983089983090

[983089983091] Z M Chen and G Q Chen ldquoEmbodied carbon dioxideemission at supra-national scale a coalition analysis or G983095BRIC and the rest o the worldrdquo Energy Policy vol 983091983097 no 983093pp 983090983096983097983097ndash983090983097983088983097 983090983088983089983089

[983089983092] H Z An X-Y Gao W Fang X Huang and Y H Ding ldquoTerole o 1047298uctuating modes o autocorrelation in crude oil pricesrdquo

Physica A vol 983091983097983091 pp 983091983096983090ndash983091983097983088 983090983088983089983092[983089983093] X-Y Gao H-Z AnH-H Liu and Y-H Ding ldquoAnalysis on the

topological properties o the linkage complex network betweencrude oil uture price and spot pricerdquo Acta Physica Sinica vol983094983088 no 983094 Article ID 983088983094983096983097983088983090 983090983088983089983089

[983089983094] X-Y Gao H Z An and W Fang ldquoResearch on 1047298uctuation o bivariate correlation o time series based on complex networkstheoryrdquo Acta Physica Sinica vol 983094983089 no 983097 Article ID 983088983097983096983097983088983090983090983088983089983090

[983089983095] S Yu and Y-M Wei ldquoPrediction o Chinarsquos coal production-environmental pollution based on a hybrid genetic algorithm-system dynamics modelrdquo Energy Policy vol 983092983090 pp 983093983090983089ndash983093983090983097983090983088983089983090

[983089983096] S Geisendor ldquoInternal selection and market selection in eco-nomic genetic algorithmsrdquo Journal of Evolutionary Economics vol 983090983089 no 983093 pp 983096983089983095ndash983096983092983089 983090983088983089983089

[983089983097] R ehrani and F Khodayar ldquoA hybrid optimized arti1047297cialintelligent model to orecast crude oil using genetic algorithmrdquo African Journal of Business Management vol 983093 pp 983089983091983089983091983088ndash983089983091983089983091983093983090983088983089983089

[983090983088] A M Elaiw X Xia and A M Shehata ldquoMinimization o uelcosts and gaseous emissions o electric power generation by model predictive controlrdquo Mathematical Problems in Engineer-ing vol 983090983088983089983091 Article ID 983097983088983094983097983093983096 983089983093 pages 983090983088983089983091

[983090983089] L Mendes P Godinho and J Dias ldquoA Forex trading systembased on a genetic algorithmrdquo Journal of Heuristics vol 983089983096 no983092 pp 983094983090983095ndash983094983093983094 983090983088983089983090

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[983090983090] M C Roberts ldquoechnical analysis and genetic programmingconstructing and testing a commodity portoliordquo Journal of Futures Markets vol 983090983093 no 983095 pp 983094983092983091ndash983094983094983088 983090983088983088983093

[983090983091] J-Y Potvin P Soriano and V Maxime ldquoGenerating tradingrules on the stock markets with genetic programmingrdquo Com- puters and Operations Research vol 983091983089 no 983095 pp 983089983088983091983091ndash983089983088983092983095983090983088983088983092

[983090983092] A Esahanipour and S Mousavi ldquoA genetic programmingmodel to generate risk-adjusted technical trading rules in stock marketsrdquo Expert Systems with Applications vol 983091983096 no 983095 pp983096983092983091983096ndash983096983092983092983093 983090983088983089983089

[983090983093] M A H Dempster W Payne Y Romahi and G W PTompson ldquoComputational learning techniques or intraday FX trading using popular technical indicatorsrdquo IEEE Transac-tions on Neural Networks vol 983089983090 no 983092 pp 983095983092983092ndash983095983093983092 983090983088983088983089

[983090983094] Nakashima Y Yokota Y Shoji and H Ishibuchi ldquoA geneticapproach to the design o autonomous agents or uturestradingrdquo Arti1047297cial Life and Robotics vol 983089983089 no 983090 pp 983089983092983093ndash983089983092983096983090983088983088983095

[983090983095] A Ghandar Z Michalewicz M Schmidt -D o and RZurbrugg ldquoComputational intelligence or evolving tradingrulesrdquo IEEE Transactions on Evolutionary Computation vol 983089983091no 983089 pp 983095983089ndash983096983094 983090983088983088983097

[983090983096] W L ung and C Quek ldquoFinancial volatility trading usinga sel-organising neural-uzzy semantic network and optionstraddle-based approachrdquo Expert Systems with Applications vol983091983096 no 983093 pp 983092983094983094983096ndash983092983094983096983096 983090983088983089983089

[983090983097] C-H Cheng -L Chen and L-Y Wei ldquoA hybrid model basedon rough sets theory and genetic algorithms or stock priceorecastingrdquo Information Sciences vol 983089983096983088 no 983097 pp 983089983094983089983088ndash983089983094983090983097983090983088983089983088

[983091983088] P-C Chang C-Y Fan and J-L Lin ldquorend discovery in1047297nancial time series data using a case based uzzy decision treerdquoExpert Systems with Applications vol 983091983096 no 983093 pp 983094983088983095983088ndash983094983088983096983088

983090983088983089983089[983091983089] G A Vasilakis K A Teo1047297latos E F Georgopoulos AKarathanasopoulos and S D Likothanassis ldquoA genetic pro-gramming approach or EURUSD exchange rate orecastingand tradingrdquo Computational Economics vol 983092983090 no 983092 pp 983092983089983093ndash983092983091983089 983090983088983089983091

[983091983090] I A Boboc and M C Dinica ldquoAn algorithm or testing theefficient market hypothesisrdquo PLoS ONE vol 983096 no 983089983088 ArticleID e983095983096983089983095983095 983090983088983089983091

[983091983091] W Cheung K S K Lam and H F Yeung ldquoIntertemporalpro1047297tability and the stability o technical analysis evidencesrom the Hong Kong stock exchangerdquo Applied Economics vol983092983091 no 983089983093 pp 983089983097983092983093ndash983089983097983094983091 983090983088983089983089

[983091983092] H Dewachter and M Lyrio ldquoTe economic value o technical

trading rules a nonparametricutility-based approachrdquo Interna-tional Journal of Finance and Economics vol 983089983088 no 983089 pp 983092983089ndash983094983090983090983088983088983093

[983091983093] A Fernandez-Perez F Fernandez-Rodrıguez and S Sosvilla-Rivero ldquoExploiting trends in the oreign exchange marketsrdquo Applied Economics Letters vol 983089983097 no 983094 pp 983093983097983089ndash983093983097983095 983090983088983089983090

[983091983094] M Metghalchia J Marcucci and Y-H Chang ldquoAre movingaverage trading rules pro1047297table Evidence rom the Europeanstock marketsrdquo Applied Economics vol 983092983092no 983089983090pp 983089983093983091983097ndash983089983093983093983097983090983088983089983090

[983091983095] C J Neely P A Weller and J M Ulrich ldquoTe adaptive mar-kets hypothesis evidence rom the oreign exchange marketrdquo Journal of Financial and Quantitative Analysis vol983092983092 no 983090pp983092983094983095ndash983092983096983096 983090983088983088983097

[983091983096] W E Shambora and R Rossiter ldquoAre there exploitable ineffi-ciencies in the utures market or oilrdquo Energy Economics vol983090983097 no 983089 pp 983089983096ndash983090983095 983090983088983088983095

[983091983097] F Allen and R Karjalainen ldquoUsing genetic algorithms to 1047297ndtechnical trading rulesrdquo Journal of Financial Economics vol 983093983089no 983090 pp 983090983092983093ndash983090983095983089 983089983097983097983097

[983092983088] J Wang ldquorading and hedging in SampP 983093983088983088 spot and uturesmarkets using genetic programmingrdquo Journal of Futures Mar-kets vol 983090983088 no 983089983088 pp 983097983089983089ndash983097983092983090 983090983088983088983088

[983092983089] J How M Ling andP Verhoeven ldquoDoes size matter A geneticprogramming approach to technical tradingrdquo QuantitativeFinance vol 983089983088 no 983090 pp 983089983091983089ndash983089983092983088 983090983088983089983088

[983092983090] F Wang P L H Yu and D W Cheung ldquoCombining technicaltrading rules using particle swarm optimizationrdquo Expert Sys-tems with Applications vol 983092983089 no 983094 pp 983091983088983089983094ndash983091983088983090983094 983090983088983089983092

[983092983091] J Andrada-Felix and F Fernandez-Rodrıguez ldquoImprovingmoving average trading rules with boosting and statisticallearning methodsrdquo Journal of Forecasting vol 983090983095 no 983093 pp 983092983091983091ndash983092983092983097 983090983088983088983096

[983092983092] -L Chong and W-K Ng ldquoechnical analysis and the

London stock exchange testing the MACD and RSI rules usingthe F983091983088rdquo Applied EconomicsLetters vol 983089983093no 983089983092pp983089983089983089983089ndash983089983089983089983092983090983088983088983096

[983092983093] I Cialenco and A Protopapadakis ldquoDo technicaltrading pro1047297tsremain in the oreign exchange market Evidence rom 983089983092 cur-renciesrdquo Journal of International Financial Markets Institutionsand Money vol 983090983089 no 983090 pp 983089983095983094ndash983090983088983094 983090983088983089983089

[983092983094] A E Milionis and E Papanagiotou ldquoDecomposing the predic-tiveperormance o the moving averagetrading rule o technicalanalysisthe contributiono linear andnon-linear dependenciesin stock returnsrdquo Journal of Applied Statistics vol 983092983088 no 983089983089 pp983090983092983096983088ndash983090983092983097983092 983090983088983089983091

[983092983095] Y S Ni J Lee and Y C Liao ldquoDo variable length movingaverage trading rules matter during a 1047297nancial crisis periodrdquo

Applied Economics Letters vol 983090983088 no 983090 pp 983089983091983093ndash983089983092983089 983090983088983089983091

[983092983096] V Pavlov and S Hurn ldquoesting the pro1047297tability o moving-average rules as a portolio selection strategyrdquo Paci1047297c-BasinFinance Journal vol 983090983088 no 983093 pp 983096983090983093ndash983096983092983090 983090983088983089983090

[983092983097] C Chiarella X-Z He and C Hommes ldquoA dynamic analysiso moving average rulesrdquo Journal of Economic Dynamics ampControl vol 983091983088 no 983097-983089983088 pp 983089983095983090983097ndash983089983095983093983091 983090983088983088983094

[983093983088] X-Z He and M Zheng ldquoDynamics o moving average rules ina continuous-time 1047297nancial market modelrdquo Journalof EconomicBehavior and Organization vol 983095983094 no 983091 pp 983094983089983093ndash983094983091983092 983090983088983089983088

[983093983089] C Neely P Weller and R Dittmar Is Technical Analysis in theForeign Exchange Market Pro1047297table A Genetic Programming Approach Cambridge University Press 983089983097983097983095

7262019 101808


Submit your manuscripts at

httpwwwhindawicom

7262019 101808



genetic algorithms to search best trading rules and pro1047297tabletechnical indicators when making investment decisions [983090983090ndash983090983093] Genetic algorithms are combined with other tools suchas the agent-based model [983090983094] uzzy math theory [983090983095] andneural networks [983090983096] Tere are also some studies that haveused genetic algorithms to orecast the price trends in the

1047297nancial market [983090983097 983091983088] or the exchange rate o the oreignexchange market [983091983089] As there are a vast number o technicaltrading rules and technical indicators available in the crudeoil utures market it is impractical to use ergodic calculationsor certain other accurate calculation methods Tereoreusing genetic algorithms is a easible way to resolve this issue

Moving average indicators have been widely used instudies o stocks and utures markets [983091983090ndash983091983095] wo movingaverages o different lengths are compared to orecast theprice trends in different markets Short moving averagesare more sensitive to price changes than long ones I ashort moving average price is higher than a long periodmoving average price traders will believe the price will riseand take long positions When the short moving averageprice alls and crosses with the long one opposite tradingactivities will be taken [983091983096] Allen and Karjalainen (AK) [983091983097]used genetic algorithms to identiy technical trading rules instock markets with daily prices o the SampP 983093983088983088 Te movingaverage price was used as one o the many indicators o thetechnical rules Other indicators such as the mean valueand maximum value are also used when making investmentdecisions Wang [983092983088] conducted similar research on spot andutures markets using genetic programing while How [983092983089]applied AKrsquos method to different cap stocks to determinethe relevance o size William comparing different technicalrules and arti1047297cial neural network (ANN) rules regarding oilutures market determined that the ANN is a good tool thuscasting doubt on the efficiency o the oil market [ 983091983096] All o these studies combine moving average indicators with otherindicators to generate trading rules However in this paperwe utilize moving averages to generate trading rules whichmay be a simple and efficient approach

Te perormance o a moving average trading rule isaffected signi1047297cantly by the period lengths [983092983090] Tereore1047297nding optimal lengths o the two periods above is a centralissue in technical analysis literature A variety o lengthshave been tried in existing research projects [983092983091ndash983092983096] In theexisting research most o moving average rules use 1047297xedmoving average period lengths and single moving averagecalculation method However it is better to use variable

lengths or different investment periods [983092983097 983093983088] and there aredifferenttypes o moving average calculation method that canbe used in technical analysis

In this paper considering that the optimal length o themoving average periods and the best calculation method may

vary rom one occasion to another we use genetic algorithmsto determine the suitable length o the moving average periodand the appropriate method Six moving average calculationmethods are considered in this paper and genetic algorithmscan help us 1047297nd out the best method and appropriate periodlengths or different circumstances Accordingly we are ableto present the most suitable moving average trading rules ortraders in the crude oil utures market

2 Data and Method

983090983089 Data We use the daily prices o the crude oil uturecontract 983089 or the period 983089983097983096983091 to 983090983088983089983091 rom the New York Mercantile Exchange (Data Source httpwwweiagovdnavpetpet pri ut s983089 dhtm) We select 983090983088 groups o sam-ple data each containing 983089983088983088983088 daily prices In the 983089983088983088983088 daily prices a 983093983088983088-day price series is used to train trading rulesin every generation Te ollowing 983090983088983088 prices are used toselect the best generated trading rule rom all generationsand the last 983091983088983088 daily prices are used to determine whetherthe generated rule can acquire excess returns Te 1047297rst groupbegins in 983089983097983096983093 the last group ends in 983090983088983089983091 and each 983089983088983088983088-day price series with a step o 983091983088983088 is selected We must alsoinclude 983093983088983088 more daily prices beore each sample series tocalculate the moving pricesor the sampleperiod Tus every independent experiment requires a 983089983093983088983088-day price series Tedata we use are presented in Figure 983089

983090983090 Method Moving average trading rules acilitatedecision-making or traders by comparing two moving

averages o different periods In this way traders can predictthe price trend by analyzing the volatility o the movingaverage prices Tere are six moving average indictors usually used in technical analysis simple moving average (SMA)weighted moving average (WMA) exponential movingaverage (EMA) adaptive moving average (AMA) typicalprice moving average (PMA) and triangular movingaverage (MA) Te calculation methods o moving averageindicators are presented in able 983089

o use a moving average trading rule in the oil uturesmarket at least three parameters must be set to establish atrading strategy Tese parameters include the lengths o twomoving average periods and the choice o the moving averagemethod rom the above sixtypes Other researchers have useddifferent lengths o sample periods in their studies In thispaper we use genetic algorithms to determine appropriatelengths o the moving average period According to existingliterature the long period is generally between 983090983088 and 983090983088983088days (very ew studies use periods longer than 983090983088983088 days)[983091983096 983091983097] and the short period is generally no longer than 983094983088days

I the long average price is lower than the short averageprice a trader will take a long position It ollows thatin opposite situations opposite strategies will be adoptedNoting the price volatility in the utures market taking a

long position when the short average price exceeds the longaverage price by at least one standard deviation in the shortperiod maybe a goodrule Conversely taking a short positionmay also be a good rule Tereore we designed the two rulesin our initial trading rules Te detailed calculation methodso the six moving averages are presented in Figure 983090

A 983089983095-binary string is used to represent a trading rulein which a seven-binary substring represents (M-N) ( isthe long period length and 1038389 is the short period length)a six-binary substring is 1038389 (1038389 belongs to the range o 983089to 983094983092) a three-binary substring represents the calculationmethod o average prices In this paper the range o to 1038389 is 983093 to 983089983091983090 Te last binary determines whether to

7262019 101808





SMA SMA (907317) = 1

minus1

9917611038389=0

11039251103925minus1038389


1038389=0 ( minus )11039251103925minus1038389

summinus1

1038389=0 ( minus )


where SC = 2(1 + )

AMA



astSC = 2(1 + 2)

slowSC = 2(1 + 30)

ER 1103925 =11039251103925 minus 11039251103925minus

sum1103925

1038389=1103925minus+1

11039251038389 minus 11039251038389minus1


3


MA MA(907317) = 1

minus1

9917611038389=0

SAM(907317 minus )

200 days

200 days

200 days

200 days 300 days

300 days

300 days

300 days

500 days

500 days

500 days 500 days

500 days

500 days

500 days 500 days


March 29 1985

June 11 1986

August 21 1987


February 26 2013

August 13 1991

June 4 1990


Period 2

Period 3

Period 21





Periods 4 5 20

F983145983143983157983154983141 983089 Data selection




Ral = sum


Ras = sum907317



begin


(983089)


7262019 101808





1 SMA

2 WMA

3 EMA

4 AMA

5 TPMA

6 TMA
























3 Results





7262019 101808



8503 89030

20

40(1)

8606 900510

20

30(2)

8708 91070

50(3)

8810 92100

50(4)

9001 93120

50(5)

9103 950210

20

30(6)

9205 960510

20

30(7)

9308 970710

20

30(8)

9410 980910

20

30(9)

9512 991210

20

30(10)

9703 01020

20

40(11)

9805 02040

20

40(12)

9907 03070

20

40(13)

0010 04090

50

100(14)

0112 05120

50

100(15)

0303 07020

50

100(16)

0405 08050

100

200(17)

0508 09070

100

200(18)

0610 10090

100

200(19)

0712 11120

100

200(20)

0903 13020

100

200(21)

F983145983143983157983154983141 983091 Sample data






1047298uctuations



7262019 101808





983089 983091 983089983090 983091983095983094983096 983088983094983094983091 minus983091983089983088983093 983091

983090 983090983088 983090983088 minus983090983097983092983094 983090983096983097983097 983093983096983092983093 983089

983091 983089983093 983089983094 983093983090983097983097 983095983095983089983095 983090983092983089983097 983089


983094 983089 983089983090 983092983097983095983094 983088983096983088983096 minus983092983089983094983096 983091

983095 983093 983089983089 983093983090983092983088 983089983096983093983092 minus983091983091983096983094 983091

983096 983089983088 983097 minus983089983089983095983093 minus983088983091983093983095 983088983096983089983096 983090

983097 983089983097 983089983090 minus983093983094983089983088 983088983094983097983089 983094983091983088983089 983089

983089983088 983088 983089983094 983089983094983091983091983096 983094983097983092983091 minus983097983091983097983094 983091

983089983089 983089 983089983091 983090983095983092983088 983088983089983090983095 minus983090983094983089983091 983091

983089983090 983089983093 983089983089 minus983089983092983090983088 minus983088983093983095983094 983088983096983092983092 983090

983089983091 983088 983095 983092983091983092983091 minus983090983090983097983094 minus983094983094983092983088 983092

983089983092 983088 983089983092 983089983092983088983094983097 983091983089983092983089 minus983089983088983097983090983096 983091

983089983093 983095 983096 983090983090983096983095 983088983090983095983091 minus983090983088983089983092 983091


983089983096 983090983088 983091 minus983097983095983092983094 minus983092983089983091983089 983093983094983089983093 983090

983089983097 983088 983088 983091983093983089983090 minus983094983088983097983089 minus983097983094983088983091 983092

983090983088 983089 983089983088 983090983097983094983096 minus983088983089983097983091 minus983091983089983094983089 983092














7262019 101808




Period 983089 983090 983091 983092 983093 983094 983095 983096 983097 983089983088 983089983089 983089983090 983089983091 983089983092 983089983093 983089983094 983089983095 983089983096 983089983097 983090983088 983090983089 Avg

Avg () 983089983088983092 983089983088983096 983094983093 983089983090983089 983089983088983089 983093983097 983093983089 983093983093 983089983092983091 983089983088983095 983089983092983088 983089983091983089 983089983089983096 983096983089 983095983096 983097983094 983089983094983088 983089983089983097 983089983089983090 983089983088983089 983095983089 983089983088983089

Avg (1038389) 983090983092 983091983094 983089983093 983092983093 983090983097 983090983097 983090983094 983089983094 983092983095 983091983095 983091983094 983092983091 983092983092 983092983095 983090983090 983089983096 983093983091 983090983092 983089983097 983091983089 983092983088 983091983090


Method Period

983089 983090 983091 983092 983093 983094 983095 983096 983097 983089983088 983089983089 983089983090 983089983091 983089983092 983089983093 983089983094 983089983095 983089983096 983089983097 983090983088 983090983089 Count

SMA 983095 983092 983089 983092 983091 983091 983095 983092 983089983088 983089 983090 983089 983089983091 983094 983091 983094983097

WMA 983089 983089 983089 983093 983091 983090 983089 983091 983094 983090983091

EMA 983089 983092 983095 983090 983090 983089983093 983091983089

AMA 983089 983089 983090983088 983089983093 983089983092 983096 983096 983090 983097 983092 983089983096 983089983094 983089983096 983090 983089 983096 983089983092983093

PMA 983096 983089983097 983089983090 983090 983091 983090 983094 983090 983089 983091 983097 983094983095

MA 983090 983092 983091 983089 983096 983089983089 983089983089 983090 983089983091 983090 983089983097 983089 983089 983095 983096983093



4 Discussion












7262019 101808




Period 983089 983090 983091 983092 983093 983094 983095 983096 983097 983089983088 983089983089 983089983090 983089983091 983089983092 983089983093 983089983094 983089983095 983089983096 983089983097 983090983088 983090983089 Count

Count 983089983097 983089983097 983090983088 983088 983093 983091 983089983091 983089983090 983088 983090 983088 983088 983089983091 983090 983088 983090 983088 983089 983090983088 983089983097 983088 983089983093983088

0

4

8

12

16

20

24

28

32

20 40 60 80 100 120 140 160 180

Mean 1009833

Median 1020000

Maximum 1940000

Minimum 6000000

Std dev 4443764

Skewness 0011466

Kurtosis 2361692

Jarque-Bera 7139346

Probability 0028165


Observations 420

F983145983143983157983154983141 983092 Distribution o

0 02 04 06 08 1

C a t e g o r y 1

C a t e g o r y 2

C a t e g o r y 3

C a t e g o r y 4

SMA

WMA

EMA

AMA

TPMA

TMA










7262019 101808











Acknowledgments


References

























7262019 101808




































7262019 101808



httpwwwhindawicom

7262019 101808





SMA SMA (907317) = 1

minus1

9917611038389=0

11039251103925minus1038389


1038389=0 ( minus )11039251103925minus1038389

summinus1

1038389=0 ( minus )


where SC = 2(1 + )

AMA



astSC = 2(1 + 2)

slowSC = 2(1 + 30)

ER 1103925 =11039251103925 minus 11039251103925minus

sum1103925

1038389=1103925minus+1

11039251038389 minus 11039251038389minus1


3


MA MA(907317) = 1

minus1

9917611038389=0

SAM(907317 minus )

200 days

200 days

200 days

200 days 300 days

300 days

300 days

300 days

500 days

500 days

500 days 500 days

500 days

500 days

500 days 500 days


March 29 1985

June 11 1986

August 21 1987


February 26 2013

August 13 1991

June 4 1990


Period 2

Period 3

Period 21





Periods 4 5 20

F983145983143983157983154983141 983089 Data selection




Ral = sum


Ras = sum907317



begin


(983089)


7262019 101808





1 SMA

2 WMA

3 EMA

4 AMA

5 TPMA

6 TMA
























3 Results





7262019 101808



8503 89030

20

40(1)

8606 900510

20

30(2)

8708 91070

50(3)

8810 92100

50(4)

9001 93120

50(5)

9103 950210

20

30(6)

9205 960510

20

30(7)

9308 970710

20

30(8)

9410 980910

20

30(9)

9512 991210

20

30(10)

9703 01020

20

40(11)

9805 02040

20

40(12)

9907 03070

20

40(13)

0010 04090

50

100(14)

0112 05120

50

100(15)

0303 07020

50

100(16)

0405 08050

100

200(17)

0508 09070

100

200(18)

0610 10090

100

200(19)

0712 11120

100

200(20)

0903 13020

100

200(21)

F983145983143983157983154983141 983091 Sample data






1047298uctuations



7262019 101808





983089 983091 983089983090 983091983095983094983096 983088983094983094983091 minus983091983089983088983093 983091

983090 983090983088 983090983088 minus983090983097983092983094 983090983096983097983097 983093983096983092983093 983089

983091 983089983093 983089983094 983093983090983097983097 983095983095983089983095 983090983092983089983097 983089


983094 983089 983089983090 983092983097983095983094 983088983096983088983096 minus983092983089983094983096 983091

983095 983093 983089983089 983093983090983092983088 983089983096983093983092 minus983091983091983096983094 983091

983096 983089983088 983097 minus983089983089983095983093 minus983088983091983093983095 983088983096983089983096 983090

983097 983089983097 983089983090 minus983093983094983089983088 983088983094983097983089 983094983091983088983089 983089

983089983088 983088 983089983094 983089983094983091983091983096 983094983097983092983091 minus983097983091983097983094 983091

983089983089 983089 983089983091 983090983095983092983088 983088983089983090983095 minus983090983094983089983091 983091

983089983090 983089983093 983089983089 minus983089983092983090983088 minus983088983093983095983094 983088983096983092983092 983090

983089983091 983088 983095 983092983091983092983091 minus983090983090983097983094 minus983094983094983092983088 983092

983089983092 983088 983089983092 983089983092983088983094983097 983091983089983092983089 minus983089983088983097983090983096 983091

983089983093 983095 983096 983090983090983096983095 983088983090983095983091 minus983090983088983089983092 983091


983089983096 983090983088 983091 minus983097983095983092983094 minus983092983089983091983089 983093983094983089983093 983090

983089983097 983088 983088 983091983093983089983090 minus983094983088983097983089 minus983097983094983088983091 983092

983090983088 983089 983089983088 983090983097983094983096 minus983088983089983097983091 minus983091983089983094983089 983092














7262019 101808




Period 983089 983090 983091 983092 983093 983094 983095 983096 983097 983089983088 983089983089 983089983090 983089983091 983089983092 983089983093 983089983094 983089983095 983089983096 983089983097 983090983088 983090983089 Avg

Avg () 983089983088983092 983089983088983096 983094983093 983089983090983089 983089983088983089 983093983097 983093983089 983093983093 983089983092983091 983089983088983095 983089983092983088 983089983091983089 983089983089983096 983096983089 983095983096 983097983094 983089983094983088 983089983089983097 983089983089983090 983089983088983089 983095983089 983089983088983089

Avg (1038389) 983090983092 983091983094 983089983093 983092983093 983090983097 983090983097 983090983094 983089983094 983092983095 983091983095 983091983094 983092983091 983092983092 983092983095 983090983090 983089983096 983093983091 983090983092 983089983097 983091983089 983092983088 983091983090


Method Period

983089 983090 983091 983092 983093 983094 983095 983096 983097 983089983088 983089983089 983089983090 983089983091 983089983092 983089983093 983089983094 983089983095 983089983096 983089983097 983090983088 983090983089 Count

SMA 983095 983092 983089 983092 983091 983091 983095 983092 983089983088 983089 983090 983089 983089983091 983094 983091 983094983097

WMA 983089 983089 983089 983093 983091 983090 983089 983091 983094 983090983091

EMA 983089 983092 983095 983090 983090 983089983093 983091983089

AMA 983089 983089 983090983088 983089983093 983089983092 983096 983096 983090 983097 983092 983089983096 983089983094 983089983096 983090 983089 983096 983089983092983093

PMA 983096 983089983097 983089983090 983090 983091 983090 983094 983090 983089 983091 983097 983094983095

MA 983090 983092 983091 983089 983096 983089983089 983089983089 983090 983089983091 983090 983089983097 983089 983089 983095 983096983093



4 Discussion












7262019 101808




Period 983089 983090 983091 983092 983093 983094 983095 983096 983097 983089983088 983089983089 983089983090 983089983091 983089983092 983089983093 983089983094 983089983095 983089983096 983089983097 983090983088 983090983089 Count

Count 983089983097 983089983097 983090983088 983088 983093 983091 983089983091 983089983090 983088 983090 983088 983088 983089983091 983090 983088 983090 983088 983089 983090983088 983089983097 983088 983089983093983088

0

4

8

12

16

20

24

28

32

20 40 60 80 100 120 140 160 180

Mean 1009833

Median 1020000

Maximum 1940000

Minimum 6000000

Std dev 4443764

Skewness 0011466

Kurtosis 2361692

Jarque-Bera 7139346

Probability 0028165


Observations 420

F983145983143983157983154983141 983092 Distribution o

0 02 04 06 08 1

C a t e g o r y 1

C a t e g o r y 2

C a t e g o r y 3

C a t e g o r y 4

SMA

WMA

EMA

AMA

TPMA

TMA










7262019 101808











Acknowledgments


References

























7262019 101808




































7262019 101808



httpwwwhindawicom

7262019 101808





1 SMA

2 WMA

3 EMA

4 AMA

5 TPMA

6 TMA
























3 Results





7262019 101808



8503 89030

20

40(1)

8606 900510

20

30(2)

8708 91070

50(3)

8810 92100

50(4)

9001 93120

50(5)

9103 950210

20

30(6)

9205 960510

20

30(7)

9308 970710

20

30(8)

9410 980910

20

30(9)

9512 991210

20

30(10)

9703 01020

20

40(11)

9805 02040

20

40(12)

9907 03070

20

40(13)

0010 04090

50

100(14)

0112 05120

50

100(15)

0303 07020

50

100(16)

0405 08050

100

200(17)

0508 09070

100

200(18)

0610 10090

100

200(19)

0712 11120

100

200(20)

0903 13020

100

200(21)

F983145983143983157983154983141 983091 Sample data






1047298uctuations



7262019 101808





983089 983091 983089983090 983091983095983094983096 983088983094983094983091 minus983091983089983088983093 983091

983090 983090983088 983090983088 minus983090983097983092983094 983090983096983097983097 983093983096983092983093 983089

983091 983089983093 983089983094 983093983090983097983097 983095983095983089983095 983090983092983089983097 983089


983094 983089 983089983090 983092983097983095983094 983088983096983088983096 minus983092983089983094983096 983091

983095 983093 983089983089 983093983090983092983088 983089983096983093983092 minus983091983091983096983094 983091

983096 983089983088 983097 minus983089983089983095983093 minus983088983091983093983095 983088983096983089983096 983090

983097 983089983097 983089983090 minus983093983094983089983088 983088983094983097983089 983094983091983088983089 983089

983089983088 983088 983089983094 983089983094983091983091983096 983094983097983092983091 minus983097983091983097983094 983091

983089983089 983089 983089983091 983090983095983092983088 983088983089983090983095 minus983090983094983089983091 983091

983089983090 983089983093 983089983089 minus983089983092983090983088 minus983088983093983095983094 983088983096983092983092 983090

983089983091 983088 983095 983092983091983092983091 minus983090983090983097983094 minus983094983094983092983088 983092

983089983092 983088 983089983092 983089983092983088983094983097 983091983089983092983089 minus983089983088983097983090983096 983091

983089983093 983095 983096 983090983090983096983095 983088983090983095983091 minus983090983088983089983092 983091


983089983096 983090983088 983091 minus983097983095983092983094 minus983092983089983091983089 983093983094983089983093 983090

983089983097 983088 983088 983091983093983089983090 minus983094983088983097983089 minus983097983094983088983091 983092

983090983088 983089 983089983088 983090983097983094983096 minus983088983089983097983091 minus983091983089983094983089 983092














7262019 101808




Period 983089 983090 983091 983092 983093 983094 983095 983096 983097 983089983088 983089983089 983089983090 983089983091 983089983092 983089983093 983089983094 983089983095 983089983096 983089983097 983090983088 983090983089 Avg

Avg () 983089983088983092 983089983088983096 983094983093 983089983090983089 983089983088983089 983093983097 983093983089 983093983093 983089983092983091 983089983088983095 983089983092983088 983089983091983089 983089983089983096 983096983089 983095983096 983097983094 983089983094983088 983089983089983097 983089983089983090 983089983088983089 983095983089 983089983088983089

Avg (1038389) 983090983092 983091983094 983089983093 983092983093 983090983097 983090983097 983090983094 983089983094 983092983095 983091983095 983091983094 983092983091 983092983092 983092983095 983090983090 983089983096 983093983091 983090983092 983089983097 983091983089 983092983088 983091983090


Method Period

983089 983090 983091 983092 983093 983094 983095 983096 983097 983089983088 983089983089 983089983090 983089983091 983089983092 983089983093 983089983094 983089983095 983089983096 983089983097 983090983088 983090983089 Count

SMA 983095 983092 983089 983092 983091 983091 983095 983092 983089983088 983089 983090 983089 983089983091 983094 983091 983094983097

WMA 983089 983089 983089 983093 983091 983090 983089 983091 983094 983090983091

EMA 983089 983092 983095 983090 983090 983089983093 983091983089

AMA 983089 983089 983090983088 983089983093 983089983092 983096 983096 983090 983097 983092 983089983096 983089983094 983089983096 983090 983089 983096 983089983092983093

PMA 983096 983089983097 983089983090 983090 983091 983090 983094 983090 983089 983091 983097 983094983095

MA 983090 983092 983091 983089 983096 983089983089 983089983089 983090 983089983091 983090 983089983097 983089 983089 983095 983096983093



4 Discussion












7262019 101808




Period 983089 983090 983091 983092 983093 983094 983095 983096 983097 983089983088 983089983089 983089983090 983089983091 983089983092 983089983093 983089983094 983089983095 983089983096 983089983097 983090983088 983090983089 Count

Count 983089983097 983089983097 983090983088 983088 983093 983091 983089983091 983089983090 983088 983090 983088 983088 983089983091 983090 983088 983090 983088 983089 983090983088 983089983097 983088 983089983093983088

0

4

8

12

16

20

24

28

32

20 40 60 80 100 120 140 160 180

Mean 1009833

Median 1020000

Maximum 1940000

Minimum 6000000

Std dev 4443764

Skewness 0011466

Kurtosis 2361692

Jarque-Bera 7139346

Probability 0028165


Observations 420

F983145983143983157983154983141 983092 Distribution o

0 02 04 06 08 1

C a t e g o r y 1

C a t e g o r y 2

C a t e g o r y 3

C a t e g o r y 4

SMA

WMA

EMA

AMA

TPMA

TMA










7262019 101808











Acknowledgments


References

























7262019 101808




































7262019 101808



httpwwwhindawicom

7262019 101808



8503 89030

20

40(1)

8606 900510

20

30(2)

8708 91070

50(3)

8810 92100

50(4)

9001 93120

50(5)

9103 950210

20

30(6)

9205 960510

20

30(7)

9308 970710

20

30(8)

9410 980910

20

30(9)

9512 991210

20

30(10)

9703 01020

20

40(11)

9805 02040

20

40(12)

9907 03070

20

40(13)

0010 04090

50

100(14)

0112 05120

50

100(15)

0303 07020

50

100(16)

0405 08050

100

200(17)

0508 09070

100

200(18)

0610 10090

100

200(19)

0712 11120

100

200(20)

0903 13020

100

200(21)

F983145983143983157983154983141 983091 Sample data






1047298uctuations



7262019 101808





983089 983091 983089983090 983091983095983094983096 983088983094983094983091 minus983091983089983088983093 983091

983090 983090983088 983090983088 minus983090983097983092983094 983090983096983097983097 983093983096983092983093 983089

983091 983089983093 983089983094 983093983090983097983097 983095983095983089983095 983090983092983089983097 983089


983094 983089 983089983090 983092983097983095983094 983088983096983088983096 minus983092983089983094983096 983091

983095 983093 983089983089 983093983090983092983088 983089983096983093983092 minus983091983091983096983094 983091

983096 983089983088 983097 minus983089983089983095983093 minus983088983091983093983095 983088983096983089983096 983090

983097 983089983097 983089983090 minus983093983094983089983088 983088983094983097983089 983094983091983088983089 983089

983089983088 983088 983089983094 983089983094983091983091983096 983094983097983092983091 minus983097983091983097983094 983091

983089983089 983089 983089983091 983090983095983092983088 983088983089983090983095 minus983090983094983089983091 983091

983089983090 983089983093 983089983089 minus983089983092983090983088 minus983088983093983095983094 983088983096983092983092 983090

983089983091 983088 983095 983092983091983092983091 minus983090983090983097983094 minus983094983094983092983088 983092

983089983092 983088 983089983092 983089983092983088983094983097 983091983089983092983089 minus983089983088983097983090983096 983091

983089983093 983095 983096 983090983090983096983095 983088983090983095983091 minus983090983088983089983092 983091


983089983096 983090983088 983091 minus983097983095983092983094 minus983092983089983091983089 983093983094983089983093 983090

983089983097 983088 983088 983091983093983089983090 minus983094983088983097983089 minus983097983094983088983091 983092

983090983088 983089 983089983088 983090983097983094983096 minus983088983089983097983091 minus983091983089983094983089 983092














7262019 101808




Period 983089 983090 983091 983092 983093 983094 983095 983096 983097 983089983088 983089983089 983089983090 983089983091 983089983092 983089983093 983089983094 983089983095 983089983096 983089983097 983090983088 983090983089 Avg

Avg () 983089983088983092 983089983088983096 983094983093 983089983090983089 983089983088983089 983093983097 983093983089 983093983093 983089983092983091 983089983088983095 983089983092983088 983089983091983089 983089983089983096 983096983089 983095983096 983097983094 983089983094983088 983089983089983097 983089983089983090 983089983088983089 983095983089 983089983088983089

Avg (1038389) 983090983092 983091983094 983089983093 983092983093 983090983097 983090983097 983090983094 983089983094 983092983095 983091983095 983091983094 983092983091 983092983092 983092983095 983090983090 983089983096 983093983091 983090983092 983089983097 983091983089 983092983088 983091983090


Method Period

983089 983090 983091 983092 983093 983094 983095 983096 983097 983089983088 983089983089 983089983090 983089983091 983089983092 983089983093 983089983094 983089983095 983089983096 983089983097 983090983088 983090983089 Count

SMA 983095 983092 983089 983092 983091 983091 983095 983092 983089983088 983089 983090 983089 983089983091 983094 983091 983094983097

WMA 983089 983089 983089 983093 983091 983090 983089 983091 983094 983090983091

EMA 983089 983092 983095 983090 983090 983089983093 983091983089

AMA 983089 983089 983090983088 983089983093 983089983092 983096 983096 983090 983097 983092 983089983096 983089983094 983089983096 983090 983089 983096 983089983092983093

PMA 983096 983089983097 983089983090 983090 983091 983090 983094 983090 983089 983091 983097 983094983095

MA 983090 983092 983091 983089 983096 983089983089 983089983089 983090 983089983091 983090 983089983097 983089 983089 983095 983096983093



4 Discussion












7262019 101808




Period 983089 983090 983091 983092 983093 983094 983095 983096 983097 983089983088 983089983089 983089983090 983089983091 983089983092 983089983093 983089983094 983089983095 983089983096 983089983097 983090983088 983090983089 Count

Count 983089983097 983089983097 983090983088 983088 983093 983091 983089983091 983089983090 983088 983090 983088 983088 983089983091 983090 983088 983090 983088 983089 983090983088 983089983097 983088 983089983093983088

0

4

8

12

16

20

24

28

32

20 40 60 80 100 120 140 160 180

Mean 1009833

Median 1020000

Maximum 1940000

Minimum 6000000

Std dev 4443764

Skewness 0011466

Kurtosis 2361692

Jarque-Bera 7139346

Probability 0028165


Observations 420

F983145983143983157983154983141 983092 Distribution o

0 02 04 06 08 1

C a t e g o r y 1

C a t e g o r y 2

C a t e g o r y 3

C a t e g o r y 4

SMA

WMA

EMA

AMA

TPMA

TMA










7262019 101808











Acknowledgments


References

























7262019 101808




































7262019 101808



httpwwwhindawicom

7262019 101808





983089 983091 983089983090 983091983095983094983096 983088983094983094983091 minus983091983089983088983093 983091

983090 983090983088 983090983088 minus983090983097983092983094 983090983096983097983097 983093983096983092983093 983089

983091 983089983093 983089983094 983093983090983097983097 983095983095983089983095 983090983092983089983097 983089


983094 983089 983089983090 983092983097983095983094 983088983096983088983096 minus983092983089983094983096 983091

983095 983093 983089983089 983093983090983092983088 983089983096983093983092 minus983091983091983096983094 983091

983096 983089983088 983097 minus983089983089983095983093 minus983088983091983093983095 983088983096983089983096 983090

983097 983089983097 983089983090 minus983093983094983089983088 983088983094983097983089 983094983091983088983089 983089

983089983088 983088 983089983094 983089983094983091983091983096 983094983097983092983091 minus983097983091983097983094 983091

983089983089 983089 983089983091 983090983095983092983088 983088983089983090983095 minus983090983094983089983091 983091

983089983090 983089983093 983089983089 minus983089983092983090983088 minus983088983093983095983094 983088983096983092983092 983090

983089983091 983088 983095 983092983091983092983091 minus983090983090983097983094 minus983094983094983092983088 983092

983089983092 983088 983089983092 983089983092983088983094983097 983091983089983092983089 minus983089983088983097983090983096 983091

983089983093 983095 983096 983090983090983096983095 983088983090983095983091 minus983090983088983089983092 983091


983089983096 983090983088 983091 minus983097983095983092983094 minus983092983089983091983089 983093983094983089983093 983090

983089983097 983088 983088 983091983093983089983090 minus983094983088983097983089 minus983097983094983088983091 983092

983090983088 983089 983089983088 983090983097983094983096 minus983088983089983097983091 minus983091983089983094983089 983092














7262019 101808




Period 983089 983090 983091 983092 983093 983094 983095 983096 983097 983089983088 983089983089 983089983090 983089983091 983089983092 983089983093 983089983094 983089983095 983089983096 983089983097 983090983088 983090983089 Avg

Avg () 983089983088983092 983089983088983096 983094983093 983089983090983089 983089983088983089 983093983097 983093983089 983093983093 983089983092983091 983089983088983095 983089983092983088 983089983091983089 983089983089983096 983096983089 983095983096 983097983094 983089983094983088 983089983089983097 983089983089983090 983089983088983089 983095983089 983089983088983089

Avg (1038389) 983090983092 983091983094 983089983093 983092983093 983090983097 983090983097 983090983094 983089983094 983092983095 983091983095 983091983094 983092983091 983092983092 983092983095 983090983090 983089983096 983093983091 983090983092 983089983097 983091983089 983092983088 983091983090


Method Period

983089 983090 983091 983092 983093 983094 983095 983096 983097 983089983088 983089983089 983089983090 983089983091 983089983092 983089983093 983089983094 983089983095 983089983096 983089983097 983090983088 983090983089 Count

SMA 983095 983092 983089 983092 983091 983091 983095 983092 983089983088 983089 983090 983089 983089983091 983094 983091 983094983097

WMA 983089 983089 983089 983093 983091 983090 983089 983091 983094 983090983091

EMA 983089 983092 983095 983090 983090 983089983093 983091983089

AMA 983089 983089 983090983088 983089983093 983089983092 983096 983096 983090 983097 983092 983089983096 983089983094 983089983096 983090 983089 983096 983089983092983093

PMA 983096 983089983097 983089983090 983090 983091 983090 983094 983090 983089 983091 983097 983094983095

MA 983090 983092 983091 983089 983096 983089983089 983089983089 983090 983089983091 983090 983089983097 983089 983089 983095 983096983093



4 Discussion












7262019 101808




Period 983089 983090 983091 983092 983093 983094 983095 983096 983097 983089983088 983089983089 983089983090 983089983091 983089983092 983089983093 983089983094 983089983095 983089983096 983089983097 983090983088 983090983089 Count

Count 983089983097 983089983097 983090983088 983088 983093 983091 983089983091 983089983090 983088 983090 983088 983088 983089983091 983090 983088 983090 983088 983089 983090983088 983089983097 983088 983089983093983088

0

4

8

12

16

20

24

28

32

20 40 60 80 100 120 140 160 180

Mean 1009833

Median 1020000

Maximum 1940000

Minimum 6000000

Std dev 4443764

Skewness 0011466

Kurtosis 2361692

Jarque-Bera 7139346

Probability 0028165


Observations 420

F983145983143983157983154983141 983092 Distribution o

0 02 04 06 08 1

C a t e g o r y 1

C a t e g o r y 2

C a t e g o r y 3

C a t e g o r y 4

SMA

WMA

EMA

AMA

TPMA

TMA










7262019 101808











Acknowledgments


References

























7262019 101808




































7262019 101808



httpwwwhindawicom

7262019 101808




Period 983089 983090 983091 983092 983093 983094 983095 983096 983097 983089983088 983089983089 983089983090 983089983091 983089983092 983089983093 983089983094 983089983095 983089983096 983089983097 983090983088 983090983089 Avg

Avg () 983089983088983092 983089983088983096 983094983093 983089983090983089 983089983088983089 983093983097 983093983089 983093983093 983089983092983091 983089983088983095 983089983092983088 983089983091983089 983089983089983096 983096983089 983095983096 983097983094 983089983094983088 983089983089983097 983089983089983090 983089983088983089 983095983089 983089983088983089

Avg (1038389) 983090983092 983091983094 983089983093 983092983093 983090983097 983090983097 983090983094 983089983094 983092983095 983091983095 983091983094 983092983091 983092983092 983092983095 983090983090 983089983096 983093983091 983090983092 983089983097 983091983089 983092983088 983091983090


Method Period

983089 983090 983091 983092 983093 983094 983095 983096 983097 983089983088 983089983089 983089983090 983089983091 983089983092 983089983093 983089983094 983089983095 983089983096 983089983097 983090983088 983090983089 Count

SMA 983095 983092 983089 983092 983091 983091 983095 983092 983089983088 983089 983090 983089 983089983091 983094 983091 983094983097

WMA 983089 983089 983089 983093 983091 983090 983089 983091 983094 983090983091

EMA 983089 983092 983095 983090 983090 983089983093 983091983089

AMA 983089 983089 983090983088 983089983093 983089983092 983096 983096 983090 983097 983092 983089983096 983089983094 983089983096 983090 983089 983096 983089983092983093

PMA 983096 983089983097 983089983090 983090 983091 983090 983094 983090 983089 983091 983097 983094983095

MA 983090 983092 983091 983089 983096 983089983089 983089983089 983090 983089983091 983090 983089983097 983089 983089 983095 983096983093



4 Discussion












7262019 101808




Period 983089 983090 983091 983092 983093 983094 983095 983096 983097 983089983088 983089983089 983089983090 983089983091 983089983092 983089983093 983089983094 983089983095 983089983096 983089983097 983090983088 983090983089 Count

Count 983089983097 983089983097 983090983088 983088 983093 983091 983089983091 983089983090 983088 983090 983088 983088 983089983091 983090 983088 983090 983088 983089 983090983088 983089983097 983088 983089983093983088

0

4

8

12

16

20

24

28

32

20 40 60 80 100 120 140 160 180

Mean 1009833

Median 1020000

Maximum 1940000

Minimum 6000000

Std dev 4443764

Skewness 0011466

Kurtosis 2361692

Jarque-Bera 7139346

Probability 0028165


Observations 420

F983145983143983157983154983141 983092 Distribution o

0 02 04 06 08 1

C a t e g o r y 1

C a t e g o r y 2

C a t e g o r y 3

C a t e g o r y 4

SMA

WMA

EMA

AMA

TPMA

TMA










7262019 101808











Acknowledgments


References

























7262019 101808




































7262019 101808



httpwwwhindawicom

7262019 101808




Period 983089 983090 983091 983092 983093 983094 983095 983096 983097 983089983088 983089983089 983089983090 983089983091 983089983092 983089983093 983089983094 983089983095 983089983096 983089983097 983090983088 983090983089 Count

Count 983089983097 983089983097 983090983088 983088 983093 983091 983089983091 983089983090 983088 983090 983088 983088 983089983091 983090 983088 983090 983088 983089 983090983088 983089983097 983088 983089983093983088

0

4

8

12

16

20

24

28

32

20 40 60 80 100 120 140 160 180

Mean 1009833

Median 1020000

Maximum 1940000

Minimum 6000000

Std dev 4443764

Skewness 0011466

Kurtosis 2361692

Jarque-Bera 7139346

Probability 0028165


Observations 420

F983145983143983157983154983141 983092 Distribution o

0 02 04 06 08 1

C a t e g o r y 1

C a t e g o r y 2

C a t e g o r y 3

C a t e g o r y 4

SMA

WMA

EMA

AMA

TPMA

TMA










7262019 101808











Acknowledgments


References

























7262019 101808




































7262019 101808



httpwwwhindawicom

7262019 101808











Acknowledgments


References

























7262019 101808




































7262019 101808



httpwwwhindawicom

7262019 101808




































7262019 101808



httpwwwhindawicom

7262019 101808



httpwwwhindawicom

Documents

101808