Research Article Integrated Model of Multiple Kernel ...downloads.hindawi.com/journals/tswj/2014/914641.pdf · Integrated Model of Multiple Kernel Learning and Differential Evolution

Research ArticleIntegrated Model of Multiple Kernel Learning andDifferential Evolution for EURUSD Trading

Shangkun Deng and Akito Sakurai

Graduate School of Science and Technology Keio University 3-14-1 Hiyoshi Kohoku-ku Yokohama 223-8522 Japan

Correspondence should be addressed to Shangkun Deng dsk8672gmailcom

Received 29 March 2014 Accepted 16 June 2014 Published 6 July 2014

Academic Editor Xin-She Yang

Copyright copy 2014 S Deng and A Sakurai This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Currency trading is an important area for individual investors government policy decisions and organization investments In thisstudy we propose a hybrid approach referred to as MKL-DE which combines multiple kernel learning (MKL) with differentialevolution (DE) for trading a currency pair MKL is used to learn a model that predicts changes in the target currency pair whereasDE is used to generate the buy and sell signals for the target currency pair based on the relative strength index (RSI) while it isalso combined with MKL as a trading signal The new hybrid implementation is applied to EURUSD trading which is the mosttraded foreign exchange (FX) currency pair MKL is essential for utilizing information from multiple information sources andDE is essential for formulating a trading rule based on a mixture of discrete structures and continuous parameters Initially thepredictionmodel optimized byMKL predicts the returns based on a technical indicator called themoving average convergence anddivergence Next a combined trading signal is optimized by DE using the inputs from the predictionmodel and technical indicatorRSI obtained frommultiple timeframesThe experimental results showed that trading using the prediction learned byMKL yieldedconsistent profits

1 Introduction

The foreign exchange (FX) market is considered to be thelargest financial market in the world In the last few decadescurrency trading has received considerable attention fromresearchers individual investors international trade com-panies and government organizations However there is aproblemwith predicting directional change in the FX becauseit is affected by many factors including financial policymarket mood or even natural disasters such as earthquakes

In general researchers use technical indicators as featuresof the raw stock prices or FX rates A technical indicator ofstock prices or FX rates is a function that returns a value forgiven prices over a given length of time in the past Thesetechnical indicators might provide traders with guidanceon whether a currency pair is oversold or overbought orwhether a trend will continue or halt Moving average (MA)[1] is the best-known technical indicator and it is also thebasis of many other trend-following or overboughtoversoldindicators The MA is inherently a follower rather than a

leader but it reflects the underlying trend in many casesManywell-known advanced technical indicators are based onthe MA such as the MACD [2] RSI [3] BIAS ratio [4] andBollinger Bands [5] In general the MACD is used to capturea trend while the RSI BIAS ratio and Bollinger Bands areused to provide an earlywarning of an overbought or oversoldcurrency pair Traders can follow the trend if it continuesbut they should also be cautious not to miss overbought oroversold signals related to the target trading stocks or cur-rency pairs

Previous researchers have used technical indicators suchas some MA based methods to identify trends or used tech-nical indicators such as the RSI William R or BIAS ratioto determine whether a target currency pair has been over-bought or oversold For example Jaruszewicz and Mandziuk[6] applied technical analysis to predict the Japanese NIKKEIindex and so they claimed that the technical indicators areuseful in a short time as a day for time horizon Deng et al[7] used several technical indicators such as RSI BIAS ratioand William R to generate trading rules by calculating

Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 914641 12 pageshttpdxdoiorg1011552014914641

2 The Scientific World Journal

a linear combination of three technical indicators and a stockprice change rate predicted value Wei et al [8] used severaltechnical indicators such as RSI MA and William R andtheir values calculated from historical prices were used asconditional features Chong andNg [9] predicted the LondonStock Exchange based on technical indicators such as theMACDandRSI to generate trading rules such as ldquoa buy signalis triggered when the RSI crosses the center line (50) frombelow while a sell signal is triggered when the RSI crossesthe center line (50) from aboverdquo and they found that tradingstrategy based on RSI or MACD obtained better returnthan buy-and-hold strategy Comparing with the previousresearch of Jaruszewicz and Mandziuk [6] and Chong andNg [9] in our proposed method we used a technical indi-cator to predict the directional change and used a technicalindicator to find overboughtoversold conditions and thento combine a directional change signal with a trade signalfrom an overboughtoversold indicator which may providemore reliable trading signal

In recent years machine learning techniques have beenused increasingly as alternative methods to help investorsor researchers forecast directional changes in stock prices orFX rates The most popular and useful methods are supportvector machines (SVMs) and genetic algorithms (GAs)Researchers often apply SVMs to predict directional changesor GAs to generate trading rules based on combinationsof trading parameters For example Kamruzzaman et al [10]used a SVMbasedmodel to predict FX rates Shioda et al [11]used a SVM formonitoring to predict the high volatility of FXrates Other researchers have used GAs to generate tradingrules For example Chang Chien and Chen [12] used a GAbased model to generate rules for stock trading by miningassociative classification rules Deng and Sakurai [13] usedGA to generate trading rules based on a technical indicatorfor FX trading Hirabayashi et al [14] used a GA to generaterules for FX intraday trading by mining features from severaltechnical indicators Esfahanipour and Mousavi [15] used aGA to generate risk-adjusted rules for trading

In addition to GAs differential evolution (DE) wasproposed by Storn and Price [16] and it is a populationbased stochastic search which functions as an efficient globaloptimizer in continuous search domainsDEhas been appliedsuccessfully in various fields For example Worasucheep [17]usedDE for forecasting the stock exchange index ofThailandTakahama et al [18] used DE to optimize neural networksfor predicting stock prices Peralta et al [19] compared DEand GA for time series prediction and showed that theperformance of DE was better than GA if more than 150generations were generated

In addition to SVMs in the last decade many researchershave used the multiple kernel learning (MKL) [20 21] toaddress the problem of selecting suitable kernels for differentfeature sets This technique mitigates the risk of erroneouskernel selection to some degree by taking a set of kernelsderiving a weight for each kernel and making better predic-tions based on the weighted sum of the kernels One of themajor advantages of MKL is that it can combine differentkernels for various input features Many researchers haveapplied MKL in their research fields For example MKL was

used by Joutou and Yanai [22] for food image recognitionForesti et al [23] used MK regression for wind speedprediction and their results outperformed those of severalconventional methods Recently researchers have used MKLfor predicting the FX rate crude oil prices and stockprices For example Deng et al [24] used MKL to fuse theinformation from stock time series and social network servicefor stock price prediction Deng and Sakurai [25] used MKLfor prediction and trading on crude oilmarkets Fletcher et al[26] used MKL for predicting the FX market from the limitorder book Luss and DrsquoAspremont [27] employed MKL forpredicting abnormal returns based on the news using textclassification Yeh et al [28] usedMKL to predict stock priceson the Taiwan stock market and they showed that MKL wasbetter than SVM for evaluating performances Deng et al[7] used MKL to predict short-term foreign exchange rateand the prediction results of MKL based method are muchbetter than conventional methods in terms of root meansquare (RMSE)Thedifference between themethod proposedin Deng et al [7] and this study is that the proposedmethod in this study uses one MKL to predict upwardtrend and uses another MKL for prediction of downwardtrend while the method in Deng et al [7] is used MKL topredict the change rates of FX rate The reason for usingone MKL to predict upward trend and using another MKLto predict downward trend is that our classification is athree-classification problem (upward trend downward trendand unknown) In addition this study uses one technicalindicator (RSI) but from three different timeframes whileDeng et al [7] used three technical indicators but from onetimeframe Deng et al [7] used multiple technical indica-tors because of the differences between different technicalindicators since they may provide different trading signalswhile this research usedmultiple timeframes of one technicalindicator since different timeframes of the same technicalindicator may provide different trading signals In additionto using individual method several researchers have usedhybrid models for trading stocks or FX rate prediction Forexample Huang and Wu [29] used SVM and GA integratedmodel for predicting a stock index Huang [30] combinedSVMwith GA to produce a stock selection model The betterperformances of the hybrid SVM-GA model than individualmethod (SVM or GA) the superiority of DE to GA [19]and superiority of MKL to SVM [22 26 28] inspired us totry a new hybrid model which combines MKL and DE It islogically expected that a MKL-DE will perform better thanthe previous methods

In the present study we use a hybrid method based onMKL and DE for prediction and to generate the tradingrules for trading currency rates In addition we noticed thatsome researchers focused on extreme returns or abnormalmovements of stock prices For example Beneish et al [31]used contextual fundamental analysis for stock predictionand they focused only on extreme returns that is returnsabove a threshold Luss and DrsquoAspremont [27] used MKLand they focused on abnormal movements which weremovements above a threshold Inspired by their researchin this study we use MKL to generate signals for upwardtrends downward trends and no trend The directional

The Scientific World Journal 3

change predictor performs learning to predict the directionof price movements The direction of movement is classifiedas an upward trend a downward trend or a probabilisticfluctuation Thus we simply set a threshold for the absolutevalues of changes below which we consider the change to bea fluctuation

In addition to trends traders also consider the possibilityof overbought or oversold conditions for the target currencypair For example if a trader predicts an upward trend butthe target currency pair is overbought that is at a highlevel it will be risky to continue following the trend Wecould use a technical indicator as a tool to determine thedegree to which the FX pair is oversold or overbought beforegenerating trading actions (buy sell or no trade) based onthe overbought or oversold signal In this study we definethe overbought or oversold signals based on a RSI (refer toSection 213)

Our trading time horizon is 1 hour which means thatwe assess overbought or oversold signals based only on 1-hour time frame data Clearly it is possible that the judg-ment would be different if we made assessments using alonger or shorter timeframe For example Figure 1 showsthe EURUSD rate and its RSI values for 1-hour and 2-hour timeframes (ie 1-hour RSI and 2-hour RSI values)Note that at the eighth point (100000 May 5 2011) inFigure 1 the 1-hour RSI value is approximately 7390 whichprovides us with a sell signal because the currency pair isoverbought whereas the 2-hour RSI value is approximately4398 which tells us that the currency is not overboughtThe rate increased further from the eighth to the ninth point(110000 May 5 2011) In addition the 1-hour RSI value isapproximately 7832 at the ninth point and the 2-hour RSIvalue is approximately 7171 which suggests that both valuesprovide overbought signals so it is highly probable that therate will decrease from the ninth point onwardsThis exampleshows that if we use the RSI to generate trading rules wemust assess the overbought or oversold conditions not onlyfor the target timeframe but also for relatively longer andshorter timeframes For example the features of the RSI froma relatively shorter timeframe (ie 30 minutes in this study)and a relatively longer timeframe (ie 2 hours) were used inthis study as suitable signals for trading a target currency pair

In the present study we use the MACD indicator oftwo currency pairs as features rather than only the targetcurrency pair and the RSI indicator from two differenttimeframes of the target trading currency pair rather thanthe target timeframe

According to the 2010 Triennial Survey (the share oftrading volume) the most heavily traded currency pairswere EURUSD 28 USDJPY 14 and GBPUSD 9TheEURUSD is the most traded currency pair in the world sothis is used as our target trading currency pair JPY and GBPare the twomost highly exchanged currencies with both USDand EUR so we also employ GBPUSD and USDJPY as sup-plementary information for predicting our target currencypair

Evaluations of the experimental results should be basedon the return-risk ratio as well as the return and the averagereturn because most investors prefer to obtain stable returns

1465

EURUSD rate

Index

Rate

2 4 6 8 10 12 14

Index2 4 6 8 10 12 14

Index2 4 6 8 10 12 14

1480

Valu

e

10305070

Valu

e

10305070

RSI 1hour (parameter n = 6)


Figure 1 Example showing the relative strength index values frommultiple timeframes

rather than high returns with high volatility that is highrisk Therefore the Sharpe ratio [32] is used as an evaluationmeasure to adjust the risk in addition to the average return

In summary this study makes three main innovations asfollows (1) to predict directional changes of EURUSD weset thresholds on the magnitude of the FX rate changes todistinguish upward trend or downward trend from randomfluctuations to predict the return whereas only a few studiesemployed this process (2) To generate a trade signal we fuseinformation frommultiple currency pairs other than only thetarget currency pair and we combined multiple RSIs frommultiple timeframes other than only the target trading time-frame whereas many previous researchers have consideredonly the target trading currency pair with a target tradingtimeframe (3) The hybrid model combined an upwardtrenddown ward trend signal with the multiple RSI signaland the hybridmodel yielded greater profits Proposedmodeloutperformed the baseline and other methods based on theresults of return and the return-risk ratio

The remainder of this paper is organized as followsSection 2 describes the background of this research Section 3explains the structure of the proposed method Section 4describes the experimental design Section 5 presents theexperimental results and provides a discussion Section 6concludes the paper

2 Background

21 Technical Indicators Technical indicators are broadlyclassified into two types trend indicators and oscillatorindicators The best-known trend indicator is the MA whichis the basis of most other indicators Next we introduce thethree technical indicators used in this study MAMACD as atrend indicator and RSI as an overboughtoversold indicator


211 SimpleMAand ExponentialMA TheMA is a techniquefor smoothing out short-term fluctuations which can beobtained by calculating the mean value of the prices over thepast 119899-periods The MA is used to understand the presenttrend which is why it is a so-called trend-following indexThere are several types of MA depending on how past pricesare weighted

The simple MA (SMA) is a simple mean value withidentical weights for past prices

SMA119899(119905) =

sum119905

119896=119905minus119899+1119875 (119896)

119899 (1)

where 119899 is the period length and 119875(119896) is the foreign exchangerate or some other value under consideration

Another type of MA the exponential MA (EMA) is themean of the underlying data which is generally the price ofa stock or foreign exchange rate for a given time period 119899where larger weights are attributed to narrower changes Thedifference between the EMA and the SMA is that the EMAis concerned more with the nearest movements which mayhave greater effects on future changes than older changesTheEMA is calculated as follows

EMA119899(119905) = 119875 (119905) lowast 119886 + (1 minus 119886) lowast EMA

119899(119905 minus 1) (2)

where EMA119899(119905) is the EMAof the rate at time 119905 and 119886 = 2(119899+

1) which is commonly used for the 119899-period EMA

212 MACD The MACD is used to predict trends in timeseries data and it provides two indicators the MACD valueand the MACD signal In general the MACD value is thedifference between the 12-period and 26-period EMAs asfollows

MACDvalue (119905) = EMA12(119905) minus EMA

26(119905) (3)

TheMACD signal is equal to the 9-period EMAof theMACDvalue as follows

MACDsignal (119905) = EMA9(MACDvalue (119905)) (4)

TheMACDparameters (12 26 and 9) can be adjusted tomeetthe needs of traders In our study we simply use the defaultMACD parameters given above because they are used widelythroughout the world

213 RSI In general traders use the RSI as a momentumoscillator to compare the magnitude of recent gains with themagnitude of recent losses If we let119875(119905) represent the closingprice on day 119905 then we can calculate the gain or loss in period119905 as follows

119866119905=

119875 (119905) minus 119875 (119905 minus 1) if 119875 (119905) gt 119875 (119905 minus 1)

0 otherwise

119871119905=

119875 (119905) minus 119875 (119905 minus 1) if 119875 (119905) lt 119875 (119905 minus 1)

0 otherwise

(5)

Next the 119899-period average gain (AG(119905)) is calculated as

AG (119905) =119899 minus 1

119899times AG (119905 minus 1) +

1

119899times 119866119905 (6)

and the 119899-period average loss (AL(119905)) is calculated as

AL (119905) = 119899 minus 1

119899times AL (119905 minus 1) + 1

119899times 119871119905 (7)

Thus the 119899-period RSI at time point 119905 is calculated as

RSI119899(119905) =

AG (119905)

AG (119905) + AL (119905)times 100 (8)

Traditionally a RSI value higher than 70 indicates that thecurrency has been overbought whereas a value below 30indicates that the currency pair has been oversold Thus theRSI provides alarm signals for investors to close the currentposition or to open a new position to buy when the currencyis oversold and to sell when it is overbought The parametersused for the overbought and oversold levels can be set up bytraders In the present study we use DE to optimize the RSIparameter

22 SVM and MKL A SVM is an optimal hyperplane usedto separate two classes or a nonlinear separating surfaceoptimized using a nonlinear mapping from the original inputspace into a high-dimensional feature space to search for anoptimally separating hyperplane in the feature spaceThe lat-ter solves classification problems that cannot be linearly sepa-rated in the input spaceWedesignate a hyperplane as optimalif it has a maximal margin where the margin is the mini-mal distance from the separating hyperplane to the closestdata points which are called the support vectors

The concept used to map the data from the originalfeature space to a high-dimensional feature space is called akernel method Finding the optimal hyperplane is formalizedas follows

min 1

21199082

+ 119862

119899

sum119894=1

120577119894

st 119910119894(⟨119908 sdot 119909

119894⟩ + 119887) ge 1 minus 120577

119894

120577119894ge 0 forall119894 = 1 2 119899

(9)

where119908 is the vector of the parameters that define the optimaldecision hyperplane ⟨119908 sdot 119909

119894⟩ + 119887 = 0 and 119887 represents the

bias (12)1199082 is considered to be a regularization termwhich controls the generalization capacities of the classifierThe second term 119862sum

119899

119894=1120577119894is the empirical risk (error) 119862 is

sometimes referred to as the soft margin parameter and itdetermines the tradeoff between the empirical risk and theregularization term Increasing the value of 119862 gives greaterimportance to empirical risk relative to the regularizationterm Positive slack variables 120577

119894allow classification errors

To extend SVM MKL uses multiple kernels to mapthe input space to a higher-dimensional feature space bycombining different kernels to obtain a better separationfunction In MKL the kernels are combined linearly and the


weight of each kernel reflects its importance The kernelscan be different kernels or the same kernels with differentparameters Each kernel in the combination may account fora different feature or a different set of features The use ofmultiple kernels can enhance the performance of the model

Suppose 119896119898(119898 = 1 119872) are 119872 positive definite

kernels on the same input space Finding the optimal decisionsurface is formalized as follows

min119908119887120577

1

2

119872

sum119898=1

1

119889119898

100381710038171003817100381711986511989810038171003817100381710038172

119867119898

+ 119862

119873

sum119894=1

120577119894

119899

sum119894=1

1198832

119894

st 119910119894(

119872

sum119898=1

⟨119865119898 Φ119898(119909119894)⟩ + 119887) ge 1 minus 120577

119894

120577119894ge 0 forall119894 = 1 2 119899

119872

sum119898=1

119889119898= 1 119889

119898ge 0

(10)

where Φ is a possibly nonlinear mapping from the inputspace to a feature space 119865

119898is the separation function is

a norm ⟨ ⟩ is the inner product 119862 is used to control thegeneralization capacities of the classifier which is selected bycrossvalidation and 119889

119898are the optimized weights

In our study the optimized weights 119889119898directly represent

the ranked relevance of each feature used in the predictionprocessWe employMKL to learn the coefficients and param-eter of the subkernels We used the multiple kernel learningtoolbox SHOGUN [21] in our experiments

In our MKL based models similarity is measured basedon the instances of EURUSD instances of USDJPY andinstances of GBPUSD We construct three similarity matri-ces for each data source These three derived similaritymatrices are also taken as three subkernels of MKL and theweights of 119889

119898EURUSD 119889119898GBPUSD and 119889119898USDJPY are learnt forthe subkernels

119896 ( 119909119894 119909119895) = 119889119898EURUSD119896EURUSD (

(1)

119894 (1)

119895)

+ 119889119898GBPUSD119896GBPUSD (

(2)

119894 (2)

119895)

+ 119889119898USDJPY119896USDJPY (

(3)

119894 (3)

119895)

(11)

where 119909119894 119894 = 1 2 119899 are training samples 119889

119898EURUSD119889119898GBPUSD and 119889119898USDJPY ge 0 and 119889

119898EURUSD + 119889119898GBPUSD +

119889119898USDJPY = 1 119909(1) are EURUSD instances 119909(2) are

GBPUSD instances and 119909(3) are USDJPY instances Inthis study 119896 is the RBF (radial basis function) kernel forSVM and MKL For other types of information sources orsubkernel combinations similar distance based similaritymatrices and kernel functions can be constructed whichare easily imported into our multikernel based learningframework

23 DE TheDE method proposed by Storn and Price [16] isa population based stochastic search approach which can beused as an efficient global optimizer in a continuous search

domain Like other evolutionary algorithms DE also has apopulation with the size 119873

119901and 119863-dimensional parameter

vectors (119863 is the number of parameters present in an objectivefunction) Two other parameters used in DE are the scalingfactor 119865 and the crossover rate 119862

119903

231 Population Structure The current population repre-sented by 119875

119909 comprises the vectors 119909(119866)

119894 which have already

been found to be acceptable either as initial points or basedon comparisons with other vectors as follows

119875(119866)

119909= (119909(119866)

119894) 119894 = 0 1 119873

119875minus 1 119866 = 0 1 119892max

119909(119866)

119894= (119909(119866)

119894119895) 119895 = 0 1 119863 minus 1

(12)

After initialization DE mutates randomly selected vectorsto produce an intermediary population 119875(119866)V of 119873

119901mutant

vectors 119881(119866)119894

Consider

119875(119866)

V = (119881(119866)

119894) 119894 = 0 1 119873

119875minus 1 119866 = 0 1 119892max

119881(119866)

119894= (119881(119866)

119894119895) 119895 = 0 1 119863 minus 1

(13)

Each vector in the current population is recombined witha mutant to produce a trial population 119875

119906of119873119901trial vectors

119906(119866)

119894 Consider

119875(119866)

119906= (119906(119866)

119894) 119894 = 0 1 119873

119875minus 1 119866 = 0 1 119892max

119906(119866)

119894= (119906(119866)

119894119895) 119895 = 0 1 119863 minus 1

(14)

232 Initialization Before the population can be initializedthe upper and lower bounds of each parameter must bespecified They can be collected into two 119863-dimensional ini-tialization vectors 119909

119880and 119909

119871 After the initialization bounds

have been specified a random number generator assignseach element of every vector with a value from the prescribedrange For example the initial value (119866 = 0) of the 119895thparameter of the 119894th vector is

119875(0)

= 119909(0)

119894119895= 119909119895119871

+ rand119895[0 1] sdot (119909

119895119880minus 119909119895119871)

119894 = 0 1 119873119875minus 1 119895 = 0 1 119863 minus 1

(15)

where rand119895[0 1] is a random number which is generated

uniformly between 0 and 1

233 Mutation After initialization DE mutates and recom-bines the population to produce a population of 119873

119901trial

vectors A mutant vector is produced according to thefollowing formulation

119881(119866)

119894119895= 119909(119866minus1)

1199031119895+ 119865 sdot (119909

(119866minus1)

1199032119895minus 119909(119866minus1)

1199033119895)

119894 = 0 1 119873119875minus 1 119895 = 0 1 119863 minus 1

(16)


The scale factor 119865 is a positive real number which controlsthe rate of population evolutionThere is no upper limit to 119865but effective values are seldom greater than 1 1199031 1199032 and 1199033refer to three randomly selected indices from the population

234 Crossover DE also employs uniform crossover Some-times referred to as discrete recombination crossover buildstrial vectors from elements that have been copied from twodifferent vectors In particular DE crosses each vector with amutant vector

119906(119866)

119894119895=

V(119866)119894119895

if (rand(119866)119894119895

le 119862119903or 119895 = 119895rand)

119909(119866minus1)

119894119895otherwise (17)

where the crossover probability 119862119903isin [0 1] is a user-defined

value which controls the fraction of elements that are copiedfrom the mutant To determine the source that contributes agiven uniform crossover compares 119862

119903to a uniform random

number rand(119866)119894119895

between 0 and 1 If the random number isless than or equal to 119862

119903 the trial element is inherited from

the mutant 119881(119866)119894

otherwise the element is copied from thevector119909(119866minus1)

119894 In addition the trial element with the randomly

selected index 119895rand is taken from the mutant to ensure thatthe trial vector does not duplicate 119909(119866)

119894

235 Selection If the trial vector 119906(119866)119894

has an equal or lowerobjective function value than that of its target vector 119909(119866)

119894 it

replaces the target vector in the next generation otherwisethe target retains its place in the population for at least onemore generation

119909(119866+1)

119894=

119906(119866)

119894if 119891 (119906(119866)

119894) le 119891 (119909

(119866)

119894)

119909(119866)

119894otherwise

(18)

236 Stopping Criteria After the new population is gener-ated the processes of mutation recombination and selectionare repeated until the optimum is obtained or a user-definedtermination criterion such as the number of generations isreached at a preset maximum 119892max

24 EvaluationMeasures In the present study we performedsimulated trading using test samples based on the tradingsignals generated by MKL prediction and the multiple RSIsignal and we evaluated the return (gain or loss) obtainedwith the proposedmodel and othermodels In general a highreturn is inevitably accompanied by the potential for highrisk Therefore investors desire a method that decreases riskwhile not decreasing the profits greatly which results in atrade-off relationship The Sharpe ratio named after WilliamForsyth Sharpe is a measure of the excess return per unitof risk in an investment asset or a trading strategy which isdefined as follows

119878 =119864 [119877 minus 119877

119891]

120590=

119864 [119877 minus 119877119891]

radicvar [119877 minus 119877119891]

(19)

where 119877 is the asset return 119877119891is the return on a benchmark

asset (usually a very low risk return such as a three-monthUStreasury bill) 120590 is the standard deviation of the asset returnand 119864[119877 minus 119877

119891] is the expected value of the excess of the asset

return relative to the benchmark asset return [32] In ourexperiments we used the Sharpe ratio as an evaluation mea-sure to assess the return-risk ratio performance of our pro-posed method with other methods

3 Proposed Method

31 Structure of the Proposed Method Figure 2 shows thestructure of the proposed method First the proposedmethod uses a MKL framework to predict directionalchanges in the currency rate based on the MACD of threecurrency pairs The RSI signals are generated using multipletimeframe features of EURUSD by considering the MKLtrading signals Finally the MKL signal and RSIs signal arecombined to produce a final decision that is the tradingsignal

The prediction and trading target currency pair in thisstudy is EURUSD We selected it as our target due tothe fact that the euro and US dollar are the two mosttraded currencies in the world representing the worldrsquos twolargest economies Therefore to better predict the changes inEURUSD is considered to contribute much to the investorsand international companies In addition to EURUSD dataitself since the two most traded currencies with USD andEUR in FXmarket are JPY andGBP USDJPY andGBPUSDare used for EURUSD predictionThese three currency pairsshare almost 50 of the FX market other currencies such asAUD (Australian dollars) CAD (Canada dollars) and CHF(Swiss Franc) are also important currencies but since theirshares in FX market are relatively small we did not considerthem in the structure of the proposed method

The trading time interval is selected to be one hour inthis study which is also selected by Hirabayashi et al [14] Tofind overboughtoversold indicator values other than target1-hour horizon data and to select some reasonable longer andshorter time horizons data are important Since the tradingtime interval is one hour 30-minute and 2-hour time horizondata are considered to be useful Too high frequency timehorizon data (such as minute data) or too low frequency timehorizon data (such as daily data) are considered to have smallimpact if we fix the trading time interval to be one hour

In this proposed method we use MKL to predict direc-tional changes and DE to find overboughtoversold informa-tion from RSI indicator Although the predicted directionalchange can be used for simulated trading in our preliminaryexperiments the accumulated profits based on just the MKLpredictions were not good enough (refer to Section 51) thesame was true for accumulated profits based on using just DEand RSI indicator Considering that the prediction and thetechnical indicatorsmight have complementary componentswe propose to combine them to get the trading signalTherefore we combineMKLandDE in the proposedmethod

32 MKL Input and Output For MKL the input features arederived from three different sources EURUSD GBPUSD


GBPUSD 1-hour MACD

1-hour MACD

Multiple kernel learning

MKL up-trendclassifier

MKL down-trendclassifier

Combination 1

Signal MKL

Combinedtrading signal

Trading signal

Combination 2

Differential evolution

Signal RSIs

RSIs signal

MKL signal

Weighted sum

2-hours RSI

1-hours RSI

30-min RSI

1-hour MACDEURUSD

USDJPY

Figure 2 Structure of the proposed method

Table 1 Features for each kernel

No Feature1 MACD-value at time 1199052 MACD-signal at time 1199053 MACD-value at time (119905 minus 1)4 MACD-signal at time (119905 minus 1)5 MACD-value at time (119905 minus 2)6 MACD-signal at time (119905 minus 2)7 MACD-value at time (119905 minus 3)8 MACD-signal at time (119905 minus 3)9 MACD-value at time (119905 minus 4)10 MACD-signal at time (119905 minus 4)11 MACD-value at time (119905 minus 5)12 MACD-signal at time (119905 minus 5)13 MACD-value at time (119905 minus 6)14 MACD-signal at time (119905 minus 6)15 MACD-value at time (119905 minus 7)16 MACD-signal at time (119905 minus 7)

and USDJPY We transform the rates to MACD signals andvalues For each kernel the inputs are the MACD valuesand MACD signals for eight consecutive periods which areshown in Table 1

Using MKL we construct two classifiers to output theMKL-up labels and the MKL-down labels (MKL-up refersto an upward trend classifier learned by MKL while MKL-down refers to a downward trend classifier learned by MKL)We want to predict directional changes in a currency with aninsensitive interval where the changes from minus01 to 01

are not considered upward or downward Thus we set twothreshold values that is 01 and minus01 which we referto as the uptrend threshold value and the downtrend valuerespectively to label the training and testing samples Therules for the MKL-up trend and MKL-down trend classifiersare shown in Table 2

Based on the predictions of these twoMKL classifiers weobtain a combined MKL signal based on the rules which areshown in Table 3The combinedMKL trading signal is one ofthe inputs for DE that needs to be combinedwith themultipleRSI signal

33 Combined Trading Signal Based on the Combined MKLand Multiple RSI Signals The multiple RSI signal valueValueRSIs is the combined value of three timeframeRSI values

ValueRSIs =3

sum119894=1

119908119894119890119894 (20)

where 119908119894are the weights of the three RSIs and 119890

119894is the value

of the RSI indicator Note that the value of the RSI indicator isexpressed as a ratio and we use RSI100 from (8)The weights119908119894of each RSI are learned by DEWe compare the RSI values in (20) with the buysell

threshold to determine themultiple RSI signalThe signal andthe condition that need to be satisfied before the signal can beissued are shown in Table 4

Signaltrading is a signal used for making decisions basedon both the combined MKL signal and the multiple RSIsignal Table 5 shows how the combined MKL and multipleRSI signal are combined to obtain the trading signal If wedecide to take a position (buy or sell) the position is retained


Table 2 Output labels for MKL up-trend and down-trend classifiers

MKL classifier MKL-trend signal Conditions

MKL-up trend MKL-up = +1 If the actual change rate is greater than the upward trend threshold valueMKL-up = minus1 If the actual change rate is less than the upward trend threshold value

MKL-down trend MKL-down = +1 If the actual change rate is less than the downward trend threshold valueMKL-down = minus1 If the actual change rate is greater than the downward trend threshold value

Table 3 Conditions for issuing the MKL signal

No Combined MKL signal(SignalMKL)

Conditions

1 No trade MKL-up = 1 and MKL-down = 12 No trade MKL-up = minus1 and MKL-down = minus13 Buy MKL-up = 1 and MKL-down = minus14 Sell MKL-up = minus1 and MKL-down = 1

Table 4 Conditions that need to be satisfied before issuing the RSIsignal

No Multiple RSI signal (SignalRSIs) Conditions1 Buy ValueRSIs lt buy threshold2 Sell ValueRSIs gt sell threshold3 No trade otherwise

Table 5 Conditions that need to be satisfied before issuing thetrading signal

Trading signal(Signaltrading)

ConditionsCombined MKL signal

(SignalMKL)Multiple RSI signal

(SignalRSIs)Buy Buy No tradeSell Sell No tradeNo trade No trade No tradeSell Any (buy sell or no trade) SellBuy Any (buy sell or no trade) Buy

for 1 hour that is we check the conditions every hour If thetrading signal (buy or sell) is the same as that 1 hour beforewe do not trade and we wait for 1 hour The data we use are 1-hour EURUSD (we used 30min data to calculate the 30minRSI value and 1-hour data to calculate the 1-hour RSI valueand the 2-hour RSI value)

34 DE Parameter Design The DE parameter vectors shownin Table 6 are used to construct the multiple RSI signals Therepresentations of the parameter vectors are as follows

(1) The first three groups represent the parameters foreach RSI (three RSIs in total) The values range from3 to 10 (integer type)

(2) Numbers 4 to 5 are used to decide the times to buysell and close positions The values range from 0 to 2(floating point number type)

Table 6 DE parameter vector design

No Value Description1 3 to 10 parameter for 1-hour RSI2 3 to 10 parameter for 2-hour RSI3 3 to 10 parameter for 30-min RSI4 0 to 2 buy threshold5 0 to 2 sell threshold6 0 to 1 weight value for 1-hour RSI7 0 to 1 weight value for 2-hour RSI8 0 to 1 weight value for 30-min RSI

(3) Numbers 6 to 8 are the weights used to linearlycombine signals which are described in (20) inSection 33 The values range from 0 to 1 (floatingpoint number type)

The population size is set to 200 and the maximumnumber of generations is set to 200 during the DE trainingstep The accumulated return obtained in the training step isselected as the objective function

4 Experiment Design

The exchange rates used in this study were obtained fromICAP The ICAP data was used in our previous study [13] fortrading on EURUSD The ICAP data use the GMT +1 hourtime zone (GMT +2 hour in summer) and they do cover theexchange rate in weekend A list of best offers best bids anddealt prices for every second are comprised in the ICAP dataWe transformed them into 30min and 1-hour timeframesWeused exchange rate data for three currency pairs from ICAPdata EURUSD GBPUSD and USDJPY We separate theoverall data into three datasets and each dataset covered theperiod from January 3 to December 30 in each year witha total of about 6200 observations (hourly data) The threedatasets used for training and testing are shown in Table 7

The data include the ldquoopen high low and closerdquo ratesduring each time interval (30min and 1 hour) The data weredivided into three disjoint datasets that covered consecutiveperiods the details of which are shown in Table 8 Nextwe divided each dataset into a training period and a testingperiod The MKL training period covered 3000 observations(around 6 months) and the testing period covered 3000observations (around 6 months) The MKL-DE training stepcovered 1500 trading hours and the MKL-DE testing stepcovered 1500 trading hours Details of the length of eachperiod are shown in Table 8


Table 7 Three datasets used for training and testing

Dataset MKL training MKL testing MKL-DE training MKL-DE testingDataset 1 (2008) Jan to Jun Jul to Dec Jul to Sep Oct to DecDataset 2 (2009) Jan to Jun Jul to Dec Jul to Sep Oct to DecDataset 3 (2010) Jan to Jun Jul to Dec Jul to Sep Oct to Dec

Table 8 Trading and testing periods for MKL and DE

Period Process Length of period1 MKL learning 3000 trading hours (around 6 months)2 MKL testing (prediction) 3000 trading hours (around 6 months)

2-1 MKL-DE training 1500 trading hours (around 3 months)2-2 MKL-DE testing (trading) 1500 trading hours (around 3 months)

Foreign exchange market is often and suddenly affectedby economic events such as a bank rate decision or evenunpredictable affair such as a big earthquake Therefore ina trading in the experiments our initial investment is 119860 USdollars For each transaction (long or short) we fix the tradingamount to be1198602US dollars with a trading leverage ratio of 2to 1 That is although we did margin transaction the tradingin our experiments is conducted with very low leverage (orwith a very high margin level) which ensures the safety ofour transaction order even though there is a big shock in FXmarket

Table 9 shows a list of themethods tested including base-linemethods proposedmethods and intermediate methodsldquoBuy and holdrdquo and ldquosell and holdrdquo were selected as baselinemethods because they are simple and well known while theyare the best methods for obtaining zero profit on average ifthe market is efficient and stationary The trading rule theyused was to buy or sell at the start of the testing period andto close the position at the end of the testing period Theother methods used for comparison comprising the simplestmethods and our proposed methods SVM-s used a kernel-ized linear model for exchange rates where the inputs werethe exchange rates of only one currency pair with SVM asa learning method SVM-m was the same as SVM-s but itutilized the features of three currency pairs MKL-m was thesame as SVM-m but the model was a multiple kernelizedlinear model that uses MKL MKL-m-t and MKL-m-t-DEwere the same as MKL-m but the prediction was changedto a three-classification problem from a two-classificationproblem The trading rule used by SVM-s SVM-m andMKL-m was to buy a currency pair when the predictionwas positive to sell when negative and ldquono traderdquo whenthe prediction was 0 The trading rule for MKL-m-t wasbased on SignalMKL The trading rule used by MKL-m-t-DEour proposed method was based on Signaltrading where theparameters were optimized using MKL and DE (see Table 5)DE-only was based on SignalRSIs that is it relied only onmultiple RSI signals The DE algorithm includes randomnumbers so we conducted 10 experiments with differentseeds for MKL-m-t-DE and DE-only In the list of methodstested since GA based method are well-known methods in

the previous literatures [12ndash14] GA-s and GA-m which areimplemented by Deng and Sakurai [13] are considered asbenchmark methods and we conducted 10 experiments withdifferent seeds for GA-s and GA-m ldquoBuy and holdrdquo andldquosell and holdrdquo are well-known baseline methods which arealso used as baseline methods by Chong and Ng [9] SVM-sSVM-mMKL-mMKL-m-t DE-only andMKL-m-t-DE areimplemented by us

5 Experimental Results and Discussion

51 Returns with the Three Datasets Table 10 shows thereturns with the methods tested where the returns weremeasured in proportion to the initial investment (the entriesin the first three columns for MKL-m-t-DE DE-only GA-s and GA-m are the average returns from 10 independentexperiments with their standard deviations) First we foundthat during the testing period (threemonths) for each datasetour proposed method yielded good average returns (about673 471 and 352) In addition our proposed methodobtained the best average return (498) among all themethods tested

Next we focused on the baseline methods ldquobuy andholdrdquo and ldquosell and holdrdquo We found that ldquobuy and holdrdquoyielded losses with all three testing datasets while ldquosell andholdrdquo yielded better returns than the other methods exceptMKL-m-t-DE during the three testing periods The ldquoselland holdrdquo strategy yielded profits during the testing periodsbecause EUR had declined against USD due to the Europeansovereign debt crisis [33] which occurred in the Eurozoneafter a big rise in EUR against USD from 2005 until the firsthalf of 2008We could not forecast the decline or surge beforethis period so we could not decide whether ldquobuy and holdrdquowas better than ldquosell and holdrdquo andwe could not conclude thatthese two naıve strategies performed well

In addition we compared the results with SVM-s andSVM-m Table 10 shows that these SVM based methodsyielded losses during all three testing periods SVM-m usedmore information (the features of three FX pairs) than SVM-s (the features of EURUSD only) in dataset 2 (2009) but the


Table 9 List of the methods tested

Method DescriptionGA-s Trade based on the trading rules optimized by GA with one RSI inputGA-m Trade based on the trading rules optimization by GA with three RSI inputBuy and hold Buy and hold until the end point of a periodSell and hold Sell and hold until the end point of a periodSVM-s Trade based on SVM prediction with one FX pair inputSVM-m Trade based on SVM prediction with three FX pairs inputMKL-m Trade based on MKL prediction with three FX pairs inputMKL-m-t Trade based on SignalMKL

DE-only Trade based on SignalRSIs (parameters are optimized by DE)MKL-m-t-DE Trade based on Signaltrading

Table 10 Returns with the methods tested (The numbers right to plusmn is the standard deviation)

Method Dataset 1 (2008) Dataset 2 (2009) Dataset 3 (2010) Average returnsGA-s 00068 plusmn 00230 minus00454 plusmn 00143 minus00284 plusmn 00569 minus00223GA-m 00098 plusmn 00991 minus00326 plusmn 00286 00087 plusmn 00241 minus00046Buy and hold minus00510 minus00426 minus00229 minus00388Sell and hold 00510 00426 00229 00388SVM-s minus02039 minus00225 minus00559 minus00941SVM-m minus00397 minus00324 minus00299 minus00340MKL-m minus01932 minus00103 00479 minus00518MKL-m-t 00216 00150 00048 00138DE-only 00035 plusmn 00991 minus00318 plusmn 00541 00082 plusmn 00131 minus00201MKL-m-t-DE 00673 plusmn 00343 00471 plusmn 00362 00352 plusmn 00215 00498

return with SVM-m (minus32) was not better than that withSVM-s (minus22)

Moreover we compared the results of proposed methodwith that of GA-s and GA-m Table 10 shows that GA-syielded positive return on average during 2008 while yieldedlosses on average during 2009 and 2010 GA-m yieldedpositive return in 2008 and 2010 but it yielded losses onaverage during 2009 and the average return of three data setsis about minus0004 which is much worse than the results of ourproposed method In addition the average return results ofGA-m for the three data sets are better than those of GA-swhich agrees with the conclusion in Deng and Sakurai [13]that the return results improved when using information ofRSI indicator from multiple timeframes

Based on the average returns we found that MKL-m-tperformed better than MKL-m which indicated that thereturns were improved by neglecting small predicted changessuch as fluctuations in the MKL-m method DE-only usedDE alone to generate the trading rules based on multipleRSI values but it yielded losses on average MKL-m-t-DEperformed the best of the four methods (MKL-m MKL-m-tMKL-m-t-DE and DE-only) which indicates that the inte-gration ofmultiple RSI signals could improve the trading per-formance

52 Sharpe Ratios In addition to the returns the Sharperatio was used to evaluate the performance of our proposedmethod and other methods We used the one-year treasury

rate as the risk-free asset to calculate the Sharpe ratio Theone-year treasury rate ranged from 17 to 43 between2008 and 2010 Next we calculated the average risk-freereturns from 2008 to 2010 and the average risk-free returnfor each testing period (three months in each year) was about075 Table 11 shows the average returns standard devia-tions and Sharpe ratios with each method (for the methodsldquoMKL-m-t-DErdquo and ldquoDE-onlyrdquo ldquoaverage returnrdquo results arethe averages of all the returns obtained from 10 experi-ments for all the testing periods with all the datasets whilethe ldquostandard deviationrdquo is the standard deviation of thesereturns)

A higher Sharpe ratio indicates a higher return or lowervolatility From Table 11 we found that for the methods ldquoGA-srdquo ldquoGA-mrdquo ldquobuy and holdrdquo ldquoSVM-srdquo ldquoSVM-mrdquo ldquoMKL-mrdquoand ldquoDE-onlyrdquo their Sharpe ratio values are negative whichindicates that their average return is less than the free-riskasset There are three methods that obtained positive Sharperatio value ldquosell and holdrdquo ldquoMKL-m-trdquo and our proposedmethod ldquoMKL-m-t-DErdquo It is clear that our proposedmethodhad a significantly higher Sharpe ratio (26111) than the othertwo methods during the testing periods The Sharpe ratioresults indicate that the proposed method is the best methodwhen evaluated by return-risk ratio

6 Conclusion and Future Work

In this study we developed a hybrid method based onMKL and DE for EURUSD trading In the first step of our


Table 11 Sharpe ratios for the baseline benchmark and proposed methods

Method Average return Standard deviation Sharpe ratioGA-s minus00223 00242 minus05025GA-m minus00046 00266 minus11177Buy and Hold minus00388 00144 minus32152Sell and Hold 00388 00144 21736SVM-s minus00941 00965 minus10528SVM-m minus00340 00050 minus83000MKL-m minus00518 01258 minus04713MKL-m-t 00138 00084 07500DE-only minus00201 00219 minus12602MKL-m-t-DE 00498 00162 26111

approach we used MKL to predict the directional changein the currency rate (with an insensitive interval) to providea combined MKL signal In the second step DE combinedthe combined MKL signal with the multiple RSI signal togenerate a trading signal The experimental results showedthat MKL-m-t yielded profits with the three testing datasets(about 138 on average) while integration of the multipleRSI signal improved the trading profits (about 498 onaverage) In addition the proposed method yielded the bestSharpe ratio (about 261) comparedwith all themodels testedwhich indicates that our proposed method outperformedother methods in terms of the return-risk ratio as well as thereturns

However there are still some unaddressed questions andsome research directions for future work For example howto find the best insensitive internal (minus01 to 01 in thisstudy) is still an open question in this study a too largeinsensitive interval could decrease the number trading timestoo much so that the trading profit also decreases whilea too small insensitive interval cannot filter the unknownmovements well the trading profit decreases For future workone may combineMKL with GA to use GA to search the bestparameters for insensitive interval in MKL automatically inorder to solve the unaddressed problems In addition otherthanRSI someother famous overboughtoversold indicatorssuch as BIAS andWilliam R could be also implemented toimprove the trading ability

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research was partially supported by the ldquoGraduateSchoolDoctoral StudentGrant-in-Aid Program2012rdquo of KeioUniversity Japan In addition the authorswish to thank ICAPfor making the data available for this research

References

[1] Online material 1 ldquoMoving averagerdquo httpenwikipediaorgwikiMoving average

[2] Online material 2 ldquoMACD Wikipediardquo httpenwikipediaorgwikiMACD

[3] Online material 3 ldquoRSIrdquo Wikipedia httpenwikipediaorgwikiRelative Strength Index

[4] Online material 5 ldquoBIAS ratiordquo Wikipedia httpenwikipediaorgwikiBias ratio 28finance29

[5] Online material 6 ldquoBollinger Bandsrdquo Wikipedia httpenwikipediaorgwikiBollinger Bands

[6] M Jaruszewicz and J Mandziuk ldquoOne day prediction ofNIKKEI index considering information from other stock mar-ketsrdquo in Proceedings of the 7th International Conference onArtificial Intelligence and SoftComputing (ICAISC rsquo04) pp 1130ndash1135 Springer Berlin Germany June 2004

[7] S Deng K Yoshiyama T Mitsubuchi and A Sakurai ldquoHybridmethod of multiple kernel learning and genetic algorithm forforecasting short-term foreign exchange ratesrdquo ComputationalEconomics pp 1ndash41 2013

[8] L Y Wei T L Chen and T H Ho ldquoA hybrid model basedon adaptive-network-based fuzzy inference system to forecastTaiwan stock marketrdquo Expert Systems with Applications vol 38no 11 pp 13625ndash13631 2011

[9] T T-L Chong and W-K Ng ldquoTechnical analysis and theLondon stock exchange testing the MACD and RSI rules usingthe FT30rdquoApplied Economics Letters vol 15 no 14 pp 1111ndash11142008

[10] J Kamruzzaman R A Sarker and I Ahmad ldquoSVM basedmodels for predicting foreign currency exchange ratesrdquo inProceedings of the 3rd IEEE International Conference on DataMining (ICDM rsquo03) pp 557ndash560Melbourne Fla USANovem-ber 2003

[11] K Shioda S Deng and A Sakurai ldquoPrediction of foreignexchange market states with support vector machinerdquo in Pro-ceedings of the 10th International Conference on Machine Learn-ing and Applications (ICMLA rsquo11) vol 1 pp 327ndash332 HonoluluHawaii USA December 2011

[12] Y Chang Chien and Y Chen ldquoMining associative classificationrules with stock trading data-A GA-based methodrdquoKnowledge-Based Systems vol 23 no 6 pp 605ndash614 2010


[13] S Deng and A Sakurai ldquoForeign exchange trading rules usinga single technical indicator from multiple timeframesrdquo inProceedings of the 27th International Conference on AdvancedInformation Networking and Applications Workshops (WAINArsquo13) pp 207ndash212 IEEE Barcelona Spain March 2013

[14] A Hirabayashi C Aranha and H Iba ldquoOptimization of thetrading rule in foreign exchange using genetic algorithmrdquo inProceedings of the 11th Annual Genetic and Evolutionary Com-putation Conference (GECCO rsquo09) pp 1529ndash1536 MontrealCanada July 2009

[15] A Esfahanipour and S Mousavi ldquoA genetic programmingmodel to generate risk-adjusted technical trading rules in stockmarketsrdquo Expert Systems with Applications vol 38 no 7 pp8438ndash8445 2011

[16] R Storn andK Price ldquoDifferential evolutionmdasha simple and effi-cient heuristic for global optimization over continuous spacesrdquoJournal of Global Optimization vol 11 no 4 pp 341ndash3591997

[17] C Worasucheep ldquoA new self adaptive differential evolutionits application in forecasting the index of stock exchange ofThailandrdquo in Proceedings of the IEEE Congress on EvolutionaryComputation (CEC rsquo07) pp 1918ndash1925 Singapore September2007

[18] T Takahama S Sakai A Hara and N Iwane ldquoPredicting stockprice using neural networks optimized by differential evolutionwith degenerationrdquo International Journal of Innovative Comput-ing Information and Control vol 5 no 12 pp 5021ndash5031 2009

[19] J Peralta X Li G Gutierrez and A Sanchis ldquoTime seriesforecasting by evolving artificial neural networks using geneticalgorithms and differential evolutionrdquo in Proceedings of theInternational Joint Conference on Neural Networks (IJCNN rsquo10)pp 1ndash8 IEEE 2010

[20] F R Bach G R G Lanckriet andM I Jordan ldquoMultiple kernellearning conic duality and the SMO algorithmrdquo in Proceedingsof the 21st International Conference onMachine Learning (ICMLrsquo04) pp 41ndash48 ACM Alberta Canada July 2004

[21] S Sonnenburg G Ratsch S Henschel et al ldquoThe SHOGUNmachine learning toolboxrdquo The Journal of Machine LearningResearch vol 11 pp 1799ndash1802 2010

[22] T Joutou and K Yanai ldquoA food image recognition system withmultiple kernel learningrdquo in Proceedings of the 16th IEEE Inter-national Conference on Image Processing (ICIP 09) pp 285ndash288IEEE November 2009

[23] L Foresti D Tuia A Pozdnoukhov andMKanevski ldquoMultiplekernel learning of environmental data Case study analysis andmapping of wind fieldsrdquo in Artificial Neural NetworksmdashICANN2009 vol 5769 of Lecture Notes in Computer Science pp 933ndash943 2009

[24] S Deng TMitsubuchi and A Sakurai ldquoStock price change rateprediction by utilizing social network activitiesrdquo The ScientificWorld Journal vol 2014 Article ID 861641 14 pages 2014

[25] S Deng and A Sakurai ldquoCrude oil spot price forecasting basedon multiple crude oil markets and timeframesrdquo Energies vol 7no 5 pp 2761ndash2779 2014

[26] T Fletcher Z Hussain and J Shawe-Taylor ldquoMultiple kernellearning on the limit order bookrdquo Journal of Machine LearningResearch-Proceedings Track vol 11 pp 167ndash174 2010

[27] R Luss and A DrsquoAspremont ldquoPredicting abnormal returnsfrom news using text classificationrdquo Quantitative Finance pp1ndash14 2012

[28] C Y Yeh CWHuang and S J Lee ldquoAmultiple-kernel supportvector regression approach for stock market price forecastingrdquo

Expert Systems with Applications vol 38 no 3 pp 2177ndash21862011

[29] S C Huang and T K Wu ldquoIntegrating GA-based time-scalefeature extractions with SVMs for stock index forecastingrdquoExpert Systems with Applications vol 35 no 4 pp 2080ndash20882008

[30] C-F Huang ldquoA hybrid stock selection model using geneticalgorithms and support vector regressionrdquo Applied Soft Com-puting vol 12 no 2 pp 807ndash818 2012

[31] M D Beneish C M Lee and R L Tarpley ldquoContextual fun-damental analysis through the prediction of extreme returnsrdquoReview of Accounting Studies vol 6 no 2-3 pp 165ndash189 2001

[32] W F SharpeThe Sharpe Ratio Streetwise-The Best of the Journalof PortfolioManagement University Press Princeton PrincetonNJ USA 1998

[33] Online material 4 ldquoEuropean sovereign debtrdquo WikipediahttpenwikipediaorgwikiEuropean sovereign-debt crisis

Submit your manuscripts athttpwwwhindawicom

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in



a linear combination of three technical indicators and a stockprice change rate predicted value Wei et al [8] used severaltechnical indicators such as RSI MA and William R andtheir values calculated from historical prices were used asconditional features Chong andNg [9] predicted the LondonStock Exchange based on technical indicators such as theMACDandRSI to generate trading rules such as ldquoa buy signalis triggered when the RSI crosses the center line (50) frombelow while a sell signal is triggered when the RSI crossesthe center line (50) from aboverdquo and they found that tradingstrategy based on RSI or MACD obtained better returnthan buy-and-hold strategy Comparing with the previousresearch of Jaruszewicz and Mandziuk [6] and Chong andNg [9] in our proposed method we used a technical indi-cator to predict the directional change and used a technicalindicator to find overboughtoversold conditions and thento combine a directional change signal with a trade signalfrom an overboughtoversold indicator which may providemore reliable trading signal

In recent years machine learning techniques have beenused increasingly as alternative methods to help investorsor researchers forecast directional changes in stock prices orFX rates The most popular and useful methods are supportvector machines (SVMs) and genetic algorithms (GAs)Researchers often apply SVMs to predict directional changesor GAs to generate trading rules based on combinationsof trading parameters For example Kamruzzaman et al [10]used a SVMbasedmodel to predict FX rates Shioda et al [11]used a SVM formonitoring to predict the high volatility of FXrates Other researchers have used GAs to generate tradingrules For example Chang Chien and Chen [12] used a GAbased model to generate rules for stock trading by miningassociative classification rules Deng and Sakurai [13] usedGA to generate trading rules based on a technical indicatorfor FX trading Hirabayashi et al [14] used a GA to generaterules for FX intraday trading by mining features from severaltechnical indicators Esfahanipour and Mousavi [15] used aGA to generate risk-adjusted rules for trading

In addition to GAs differential evolution (DE) wasproposed by Storn and Price [16] and it is a populationbased stochastic search which functions as an efficient globaloptimizer in continuous search domainsDEhas been appliedsuccessfully in various fields For example Worasucheep [17]usedDE for forecasting the stock exchange index ofThailandTakahama et al [18] used DE to optimize neural networksfor predicting stock prices Peralta et al [19] compared DEand GA for time series prediction and showed that theperformance of DE was better than GA if more than 150generations were generated

In addition to SVMs in the last decade many researchershave used the multiple kernel learning (MKL) [20 21] toaddress the problem of selecting suitable kernels for differentfeature sets This technique mitigates the risk of erroneouskernel selection to some degree by taking a set of kernelsderiving a weight for each kernel and making better predic-tions based on the weighted sum of the kernels One of themajor advantages of MKL is that it can combine differentkernels for various input features Many researchers haveapplied MKL in their research fields For example MKL was

used by Joutou and Yanai [22] for food image recognitionForesti et al [23] used MK regression for wind speedprediction and their results outperformed those of severalconventional methods Recently researchers have used MKLfor predicting the FX rate crude oil prices and stockprices For example Deng et al [24] used MKL to fuse theinformation from stock time series and social network servicefor stock price prediction Deng and Sakurai [25] used MKLfor prediction and trading on crude oilmarkets Fletcher et al[26] used MKL for predicting the FX market from the limitorder book Luss and DrsquoAspremont [27] employed MKL forpredicting abnormal returns based on the news using textclassification Yeh et al [28] usedMKL to predict stock priceson the Taiwan stock market and they showed that MKL wasbetter than SVM for evaluating performances Deng et al[7] used MKL to predict short-term foreign exchange rateand the prediction results of MKL based method are muchbetter than conventional methods in terms of root meansquare (RMSE)Thedifference between themethod proposedin Deng et al [7] and this study is that the proposedmethod in this study uses one MKL to predict upwardtrend and uses another MKL for prediction of downwardtrend while the method in Deng et al [7] is used MKL topredict the change rates of FX rate The reason for usingone MKL to predict upward trend and using another MKLto predict downward trend is that our classification is athree-classification problem (upward trend downward trendand unknown) In addition this study uses one technicalindicator (RSI) but from three different timeframes whileDeng et al [7] used three technical indicators but from onetimeframe Deng et al [7] used multiple technical indica-tors because of the differences between different technicalindicators since they may provide different trading signalswhile this research usedmultiple timeframes of one technicalindicator since different timeframes of the same technicalindicator may provide different trading signals In additionto using individual method several researchers have usedhybrid models for trading stocks or FX rate prediction Forexample Huang and Wu [29] used SVM and GA integratedmodel for predicting a stock index Huang [30] combinedSVMwith GA to produce a stock selection model The betterperformances of the hybrid SVM-GA model than individualmethod (SVM or GA) the superiority of DE to GA [19]and superiority of MKL to SVM [22 26 28] inspired us totry a new hybrid model which combines MKL and DE It islogically expected that a MKL-DE will perform better thanthe previous methods

In the present study we use a hybrid method based onMKL and DE for prediction and to generate the tradingrules for trading currency rates In addition we noticed thatsome researchers focused on extreme returns or abnormalmovements of stock prices For example Beneish et al [31]used contextual fundamental analysis for stock predictionand they focused only on extreme returns that is returnsabove a threshold Luss and DrsquoAspremont [27] used MKLand they focused on abnormal movements which weremovements above a threshold Inspired by their researchin this study we use MKL to generate signals for upwardtrends downward trends and no trend The directional








1465

EURUSD rate

Index

Rate

2 4 6 8 10 12 14

Index2 4 6 8 10 12 14

Index2 4 6 8 10 12 14

1480

Valu

e

10305070

Valu

e

10305070







2 Background





SMA119899(119905) =

sum119905

119896=119905minus119899+1119875 (119896)

119899 (1)




119899(119905 minus 1) (2)





26(119905) (3)





119866119905=


0 otherwise

119871119905=


0 otherwise

(5)


AG (119905) =119899 minus 1

119899times AG (119905 minus 1) +

1

119899times 119866119905 (6)


AL (119905) = 119899 minus 1

119899times AL (119905 minus 1) + 1

119899times 119871119905 (7)


RSI119899(119905) =

AG (119905)

AG (119905) + AL (119905)times 100 (8)




min 1

21199082

+ 119862

119899

sum119894=1

120577119894

st 119910119894(⟨119908 sdot 119909

119894⟩ + 119887) ge 1 minus 120577

119894

120577119894ge 0 forall119894 = 1 2 119899

(9)




119899









min119908119887120577

1

2

119872

sum119898=1

1

119889119898

100381710038171003817100381711986511989810038171003817100381710038172

119867119898

+ 119862

119873

sum119894=1

120577119894

119899

sum119894=1

1198832

119894

st 119910119894(

119872

sum119898=1

⟨119865119898 Φ119898(119909119894)⟩ + 119887) ge 1 minus 120577

119894

120577119894ge 0 forall119894 = 1 2 119899

119872

sum119898=1

119889119898= 1 119889

119898ge 0

(10)









119896 ( 119909119894 119909119895) = 119889119898EURUSD119896EURUSD (

(1)

119894 (1)

119895)

+ 119889119898GBPUSD119896GBPUSD (

(2)

119894 (2)

119895)

+ 119889119898USDJPY119896USDJPY (

(3)

119894 (3)

119895)

(11)



119898EURUSD + 119889119898GBPUSD +







119903





119875(119866)

119909= (119909(119866)

119894) 119894 = 0 1 119873

119875minus 1 119866 = 0 1 119892max

119909(119866)

119894= (119909(119866)

119894119895) 119895 = 0 1 119863 minus 1

(12)


119901mutant

vectors 119881(119866)119894

Consider

119875(119866)

V = (119881(119866)

119894) 119894 = 0 1 119873

119875minus 1 119866 = 0 1 119892max

119881(119866)

119894= (119881(119866)

119894119895) 119895 = 0 1 119863 minus 1

(13)



119906(119866)

119894 Consider

119875(119866)

119906= (119906(119866)

119894) 119894 = 0 1 119873

119875minus 1 119866 = 0 1 119892max

119906(119866)

119894= (119906(119866)

119894119895) 119895 = 0 1 119863 minus 1

(14)


119880and 119909



119875(0)

= 119909(0)

119894119895= 119909119895119871

+ rand119895[0 1] sdot (119909

119895119880minus 119909119895119871)

119894 = 0 1 119873119875minus 1 119895 = 0 1 119863 minus 1

(15)




119901trial


119881(119866)

119894119895= 119909(119866minus1)

1199031119895+ 119865 sdot (119909

(119866minus1)

1199032119895minus 119909(119866minus1)

1199033119895)

119894 = 0 1 119873119875minus 1 119895 = 0 1 119863 minus 1

(16)




119906(119866)

119894119895=

V(119866)119894119895

if (rand(119866)119894119895

le 119862119903or 119895 = 119895rand)

119909(119866minus1)

119894119895otherwise (17)




number rand(119866)119894119895



the mutant 119881(119866)119894




119894



119894 it


119909(119866+1)

119894=

119906(119866)

119894if 119891 (119906(119866)

119894) le 119891 (119909

(119866)

119894)

119909(119866)

119894otherwise

(18)



119878 =119864 [119877 minus 119877

119891]

120590=

119864 [119877 minus 119877119891]

radicvar [119877 minus 119877119891]

(19)





3 Proposed Method







GBPUSD 1-hour MACD

1-hour MACD




Combination 1

Signal MKL


Trading signal

Combination 2


Signal RSIs

RSIs signal

MKL signal

Weighted sum

2-hours RSI

1-hours RSI

30-min RSI

1-hour MACDEURUSD

USDJPY









ValueRSIs =3

sum119894=1

119908119894119890119894 (20)


119894is the value











Conditions

















4 Experiment Design





































Acknowledgments


References











































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in










1465

EURUSD rate

Index

Rate

2 4 6 8 10 12 14

Index2 4 6 8 10 12 14

Index2 4 6 8 10 12 14

1480

Valu

e

10305070

Valu

e

10305070







2 Background





SMA119899(119905) =

sum119905

119896=119905minus119899+1119875 (119896)

119899 (1)




119899(119905 minus 1) (2)





26(119905) (3)





119866119905=


0 otherwise

119871119905=


0 otherwise

(5)


AG (119905) =119899 minus 1

119899times AG (119905 minus 1) +

1

119899times 119866119905 (6)


AL (119905) = 119899 minus 1

119899times AL (119905 minus 1) + 1

119899times 119871119905 (7)


RSI119899(119905) =

AG (119905)

AG (119905) + AL (119905)times 100 (8)




min 1

21199082

+ 119862

119899

sum119894=1

120577119894

st 119910119894(⟨119908 sdot 119909

119894⟩ + 119887) ge 1 minus 120577

119894

120577119894ge 0 forall119894 = 1 2 119899

(9)




119899









min119908119887120577

1

2

119872

sum119898=1

1

119889119898

100381710038171003817100381711986511989810038171003817100381710038172

119867119898

+ 119862

119873

sum119894=1

120577119894

119899

sum119894=1

1198832

119894

st 119910119894(

119872

sum119898=1

⟨119865119898 Φ119898(119909119894)⟩ + 119887) ge 1 minus 120577

119894

120577119894ge 0 forall119894 = 1 2 119899

119872

sum119898=1

119889119898= 1 119889

119898ge 0

(10)









119896 ( 119909119894 119909119895) = 119889119898EURUSD119896EURUSD (

(1)

119894 (1)

119895)

+ 119889119898GBPUSD119896GBPUSD (

(2)

119894 (2)

119895)

+ 119889119898USDJPY119896USDJPY (

(3)

119894 (3)

119895)

(11)



119898EURUSD + 119889119898GBPUSD +







119903





119875(119866)

119909= (119909(119866)

119894) 119894 = 0 1 119873

119875minus 1 119866 = 0 1 119892max

119909(119866)

119894= (119909(119866)

119894119895) 119895 = 0 1 119863 minus 1

(12)


119901mutant

vectors 119881(119866)119894

Consider

119875(119866)

V = (119881(119866)

119894) 119894 = 0 1 119873

119875minus 1 119866 = 0 1 119892max

119881(119866)

119894= (119881(119866)

119894119895) 119895 = 0 1 119863 minus 1

(13)



119906(119866)

119894 Consider

119875(119866)

119906= (119906(119866)

119894) 119894 = 0 1 119873

119875minus 1 119866 = 0 1 119892max

119906(119866)

119894= (119906(119866)

119894119895) 119895 = 0 1 119863 minus 1

(14)


119880and 119909



119875(0)

= 119909(0)

119894119895= 119909119895119871

+ rand119895[0 1] sdot (119909

119895119880minus 119909119895119871)

119894 = 0 1 119873119875minus 1 119895 = 0 1 119863 minus 1

(15)




119901trial


119881(119866)

119894119895= 119909(119866minus1)

1199031119895+ 119865 sdot (119909

(119866minus1)

1199032119895minus 119909(119866minus1)

1199033119895)

119894 = 0 1 119873119875minus 1 119895 = 0 1 119863 minus 1

(16)




119906(119866)

119894119895=

V(119866)119894119895

if (rand(119866)119894119895

le 119862119903or 119895 = 119895rand)

119909(119866minus1)

119894119895otherwise (17)




number rand(119866)119894119895



the mutant 119881(119866)119894




119894



119894 it


119909(119866+1)

119894=

119906(119866)

119894if 119891 (119906(119866)

119894) le 119891 (119909

(119866)

119894)

119909(119866)

119894otherwise

(18)



119878 =119864 [119877 minus 119877

119891]

120590=

119864 [119877 minus 119877119891]

radicvar [119877 minus 119877119891]

(19)





3 Proposed Method







GBPUSD 1-hour MACD

1-hour MACD




Combination 1

Signal MKL


Trading signal

Combination 2


Signal RSIs

RSIs signal

MKL signal

Weighted sum

2-hours RSI

1-hours RSI

30-min RSI

1-hour MACDEURUSD

USDJPY









ValueRSIs =3

sum119894=1

119908119894119890119894 (20)


119894is the value











Conditions

















4 Experiment Design





































Acknowledgments


References











































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in






SMA119899(119905) =

sum119905

119896=119905minus119899+1119875 (119896)

119899 (1)




119899(119905 minus 1) (2)





26(119905) (3)





119866119905=


0 otherwise

119871119905=


0 otherwise

(5)


AG (119905) =119899 minus 1

119899times AG (119905 minus 1) +

1

119899times 119866119905 (6)


AL (119905) = 119899 minus 1

119899times AL (119905 minus 1) + 1

119899times 119871119905 (7)


RSI119899(119905) =

AG (119905)

AG (119905) + AL (119905)times 100 (8)




min 1

21199082

+ 119862

119899

sum119894=1

120577119894

st 119910119894(⟨119908 sdot 119909

119894⟩ + 119887) ge 1 minus 120577

119894

120577119894ge 0 forall119894 = 1 2 119899

(9)




119899









min119908119887120577

1

2

119872

sum119898=1

1

119889119898

100381710038171003817100381711986511989810038171003817100381710038172

119867119898

+ 119862

119873

sum119894=1

120577119894

119899

sum119894=1

1198832

119894

st 119910119894(

119872

sum119898=1

⟨119865119898 Φ119898(119909119894)⟩ + 119887) ge 1 minus 120577

119894

120577119894ge 0 forall119894 = 1 2 119899

119872

sum119898=1

119889119898= 1 119889

119898ge 0

(10)









119896 ( 119909119894 119909119895) = 119889119898EURUSD119896EURUSD (

(1)

119894 (1)

119895)

+ 119889119898GBPUSD119896GBPUSD (

(2)

119894 (2)

119895)

+ 119889119898USDJPY119896USDJPY (

(3)

119894 (3)

119895)

(11)



119898EURUSD + 119889119898GBPUSD +







119903





119875(119866)

119909= (119909(119866)

119894) 119894 = 0 1 119873

119875minus 1 119866 = 0 1 119892max

119909(119866)

119894= (119909(119866)

119894119895) 119895 = 0 1 119863 minus 1

(12)


119901mutant

vectors 119881(119866)119894

Consider

119875(119866)

V = (119881(119866)

119894) 119894 = 0 1 119873

119875minus 1 119866 = 0 1 119892max

119881(119866)

119894= (119881(119866)

119894119895) 119895 = 0 1 119863 minus 1

(13)



119906(119866)

119894 Consider

119875(119866)

119906= (119906(119866)

119894) 119894 = 0 1 119873

119875minus 1 119866 = 0 1 119892max

119906(119866)

119894= (119906(119866)

119894119895) 119895 = 0 1 119863 minus 1

(14)


119880and 119909



119875(0)

= 119909(0)

119894119895= 119909119895119871

+ rand119895[0 1] sdot (119909

119895119880minus 119909119895119871)

119894 = 0 1 119873119875minus 1 119895 = 0 1 119863 minus 1

(15)




119901trial


119881(119866)

119894119895= 119909(119866minus1)

1199031119895+ 119865 sdot (119909

(119866minus1)

1199032119895minus 119909(119866minus1)

1199033119895)

119894 = 0 1 119873119875minus 1 119895 = 0 1 119863 minus 1

(16)




119906(119866)

119894119895=

V(119866)119894119895

if (rand(119866)119894119895

le 119862119903or 119895 = 119895rand)

119909(119866minus1)

119894119895otherwise (17)




number rand(119866)119894119895



the mutant 119881(119866)119894




119894



119894 it


119909(119866+1)

119894=

119906(119866)

119894if 119891 (119906(119866)

119894) le 119891 (119909

(119866)

119894)

119909(119866)

119894otherwise

(18)



119878 =119864 [119877 minus 119877

119891]

120590=

119864 [119877 minus 119877119891]

radicvar [119877 minus 119877119891]

(19)





3 Proposed Method







GBPUSD 1-hour MACD

1-hour MACD




Combination 1

Signal MKL


Trading signal

Combination 2


Signal RSIs

RSIs signal

MKL signal

Weighted sum

2-hours RSI

1-hours RSI

30-min RSI

1-hour MACDEURUSD

USDJPY









ValueRSIs =3

sum119894=1

119908119894119890119894 (20)


119894is the value











Conditions

















4 Experiment Design





































Acknowledgments


References











































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in







min119908119887120577

1

2

119872

sum119898=1

1

119889119898

100381710038171003817100381711986511989810038171003817100381710038172

119867119898

+ 119862

119873

sum119894=1

120577119894

119899

sum119894=1

1198832

119894

st 119910119894(

119872

sum119898=1

⟨119865119898 Φ119898(119909119894)⟩ + 119887) ge 1 minus 120577

119894

120577119894ge 0 forall119894 = 1 2 119899

119872

sum119898=1

119889119898= 1 119889

119898ge 0

(10)









119896 ( 119909119894 119909119895) = 119889119898EURUSD119896EURUSD (

(1)

119894 (1)

119895)

+ 119889119898GBPUSD119896GBPUSD (

(2)

119894 (2)

119895)

+ 119889119898USDJPY119896USDJPY (

(3)

119894 (3)

119895)

(11)



119898EURUSD + 119889119898GBPUSD +







119903





119875(119866)

119909= (119909(119866)

119894) 119894 = 0 1 119873

119875minus 1 119866 = 0 1 119892max

119909(119866)

119894= (119909(119866)

119894119895) 119895 = 0 1 119863 minus 1

(12)


119901mutant

vectors 119881(119866)119894

Consider

119875(119866)

V = (119881(119866)

119894) 119894 = 0 1 119873

119875minus 1 119866 = 0 1 119892max

119881(119866)

119894= (119881(119866)

119894119895) 119895 = 0 1 119863 minus 1

(13)



119906(119866)

119894 Consider

119875(119866)

119906= (119906(119866)

119894) 119894 = 0 1 119873

119875minus 1 119866 = 0 1 119892max

119906(119866)

119894= (119906(119866)

119894119895) 119895 = 0 1 119863 minus 1

(14)


119880and 119909



119875(0)

= 119909(0)

119894119895= 119909119895119871

+ rand119895[0 1] sdot (119909

119895119880minus 119909119895119871)

119894 = 0 1 119873119875minus 1 119895 = 0 1 119863 minus 1

(15)




119901trial


119881(119866)

119894119895= 119909(119866minus1)

1199031119895+ 119865 sdot (119909

(119866minus1)

1199032119895minus 119909(119866minus1)

1199033119895)

119894 = 0 1 119873119875minus 1 119895 = 0 1 119863 minus 1

(16)




119906(119866)

119894119895=

V(119866)119894119895

if (rand(119866)119894119895

le 119862119903or 119895 = 119895rand)

119909(119866minus1)

119894119895otherwise (17)




number rand(119866)119894119895



the mutant 119881(119866)119894




119894



119894 it


119909(119866+1)

119894=

119906(119866)

119894if 119891 (119906(119866)

119894) le 119891 (119909

(119866)

119894)

119909(119866)

119894otherwise

(18)



119878 =119864 [119877 minus 119877

119891]

120590=

119864 [119877 minus 119877119891]

radicvar [119877 minus 119877119891]

(19)





3 Proposed Method







GBPUSD 1-hour MACD

1-hour MACD




Combination 1

Signal MKL


Trading signal

Combination 2


Signal RSIs

RSIs signal

MKL signal

Weighted sum

2-hours RSI

1-hours RSI

30-min RSI

1-hour MACDEURUSD

USDJPY









ValueRSIs =3

sum119894=1

119908119894119890119894 (20)


119894is the value











Conditions

















4 Experiment Design





































Acknowledgments


References











































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in






119906(119866)

119894119895=

V(119866)119894119895

if (rand(119866)119894119895

le 119862119903or 119895 = 119895rand)

119909(119866minus1)

119894119895otherwise (17)




number rand(119866)119894119895



the mutant 119881(119866)119894




119894



119894 it


119909(119866+1)

119894=

119906(119866)

119894if 119891 (119906(119866)

119894) le 119891 (119909

(119866)

119894)

119909(119866)

119894otherwise

(18)



119878 =119864 [119877 minus 119877

119891]

120590=

119864 [119877 minus 119877119891]

radicvar [119877 minus 119877119891]

(19)





3 Proposed Method







GBPUSD 1-hour MACD

1-hour MACD




Combination 1

Signal MKL


Trading signal

Combination 2


Signal RSIs

RSIs signal

MKL signal

Weighted sum

2-hours RSI

1-hours RSI

30-min RSI

1-hour MACDEURUSD

USDJPY









ValueRSIs =3

sum119894=1

119908119894119890119894 (20)


119894is the value











Conditions

















4 Experiment Design





































Acknowledgments


References











































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




GBPUSD 1-hour MACD

1-hour MACD




Combination 1

Signal MKL


Trading signal

Combination 2


Signal RSIs

RSIs signal

MKL signal

Weighted sum

2-hours RSI

1-hours RSI

30-min RSI

1-hour MACDEURUSD

USDJPY









ValueRSIs =3

sum119894=1

119908119894119890119894 (20)


119894is the value











Conditions

















4 Experiment Design





































Acknowledgments


References











































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in










Conditions

















4 Experiment Design





































Acknowledgments


References











































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





































Acknowledgments


References











































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in
























Acknowledgments


References











































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in










Acknowledgments


References











































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in

































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in










Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in



Documents

Research Article Integrated Model of Multiple Kernel ...downloads.hindawi.com/journals/tswj/2014/914641.pdf · Integrated Model of Multiple Kernel Learning and Differential Evolution