Hndaw Publshng Corporaton e Scentfc World Journal, Artcle ID 914641, 12 pages http://dx.do.org/10.1155/2014/914641 Research Artcle Integrated Model of Multple Kernel Learnng and Dfferental Evoluton for EUR/USD Tradng Shangkun Deng and Akto Sakura Graduate School of Scence and Technology, Keo Unversty, 3-14-1 Hyosh, Kohoku-ku, Yokohama 223-8522, Japan Correspondence should be addressed to Shangkun Deng; dsk8672@gmal.com Receved 29 March 2014; Accepted 16 June 2014; Publshed 6 July 2014 Academc Edtor: Xn-She Yang Copyrght 2014 S. Deng and A. Sakura. Ths s an open access artcle dstrbuted under the Creatve Commons Attrbuton Lcense, whch permts unrestrcted use, dstrbuton, and reproducton n any medum, provded the orgnal work s properly cted. Currency tradng s an mportant area for ndvdual nvestors, government polcy decsons, and organzaton nvestments. In ths study, we propose a hybrd approach referred to as MKL-DE, whch combnes multple kernel learnng (MKL) wth dfferental evoluton (DE) for tradng a currency par. MKL s used to learn a model that predcts changes n the target currency par, whereas DE s used to generate the buy and sell sgnals for the target currency par based on the relatve strength ndex (RSI), whle t s also combned wth MKL as a tradng sgnal. The new hybrd mplementaton s appled to EUR/USD tradng, whch s the most traded foregn exchange (FX) currency par. MKL s essental for utlzng nformaton from multple nformaton sources and DE s essental for formulatng a tradng rule based on a mxture of dscrete structures and contnuous parameters. Intally, the predcton model optmzed by MKL predcts the returns based on a techncal ndcator called the movng average convergence and dvergence. Next, a combned tradng sgnal s optmzed byde usng the nputs from the predcton model and techncal ndcator RSI obtaned from multple tmeframes. The expermental results showed that tradng usng the predcton learned by MKL yelded consstent profts. 1. Introducton The foregn exchange (FX) market s consdered to be the largest fnancal market n the world. In the last few decades, currency tradng has receved consderable attenton from researchers, ndvdual nvestors, nternatonal trade companes, and government organzatons. However, there s a problem wth predctng drectonal change n the FX because t s affected by many factors, ncludng fnancal polcy, market mood, or even natural dsasters such as earthquakes. In general, researchers use techncal ndcators as features of the raw stock prces or FX rates. A techncal ndcator of stock prces or FX rates s a functon that returns a value for gven prces over a gven length of tme n the past. These techncal ndcators mght provde traders wth gudance on whether a currency par s oversold or overbought, or whether a trend wll contnue or halt. Movng average (MA) [1] s the best-known techncal ndcator and t s also the bass of many other trend-followng or overbought/oversold ndcators. The MA s nherently a follower rather than a leader, but t reflects the underlyng trend n many cases. Many well-known advanced techncal ndcators are based on the MA, such as the MACD [2], RSI [3], BIAS rato [4], and Bollnger Bands [5]. In general, the MACD s used to capture a trend whle the RSI, BIAS rato, and Bollnger Bands are used to provde an early warnng of an overbought or oversold currency par. Traders can follow the trend f t contnues but they should also be cautous not to mss overbought or oversold sgnals related to the target tradng stocks or currency pars. Prevous researchers have used techncal ndcators such as some MA based methods to dentfy trends or used techncal ndcators such as the RSI, Wllam %R, or BIAS rato to determne whether a target currency par has been overbought or oversold. For example, Jaruszewcz and Mańdzuk [6] appled techncal analyss to predct the Japanese NIKKEI ndex and so they clamed that the techncal ndcators are useful n a short tme as a day for tme horzon. Deng et al. [7] used several techncal ndcators such as RSI, BIAS rato, and Wllam %R to generate tradng rules by calculatng
2 The Scentfc World Journal a lnear combnaton of three techncal ndcators and a stock prcechangeratepredctedvalue.weetal.[8] usedseveral techncal ndcators such as RSI, MA, and Wllam %R and ther values calculated from hstorcal prces were used as condtonal features. Chong and Ng [9] predcted the London Stock Exchange based on techncal ndcators such as the MACD and RSI to generate tradng rules, such as a buy sgnal s trggered when the RSI crosses the center lne (50) from below, whle a sell sgnal s trggered when the RSI crosses the center lne (50) from above, and they found that tradng strategy based on RSI or MACD obtaned better return than buy-and-hold strategy. Comparng wth the prevous research of Jaruszewcz and Mańdzuk [6] and Chong and Ng [9], n our proposed method, we used a techncal ndcator to predct the drectonal change and used a techncal ndcator to fnd overbought/oversold condtons and then to combne a drectonal change sgnal wth a trade sgnal from an overbought/oversold ndcator, whch may provde more relable tradng sgnal. In recent years, machne learnng technques have been used ncreasngly as alternatve methods to help nvestors or researchers forecast drectonal changes n stock prces or FX rates. The most popular and useful methods are support vector machnes (SVMs) and genetc algorthms (GAs). Researchers often apply SVMs to predct drectonal changes or GAs to generate tradng rules based on combnatons of tradng parameters. For example, Kamruzzaman et al. [10] used a SVM based model to predct FX rates. Shoda et al. [11] used a SVM for montorng to predct the hgh volatlty of FX rates. Other researchers have used GAs to generate tradng rules. For example, Chang Chen and Chen [12] usedaga based model to generate rules for stock tradng by mnng assocatve classfcaton rules. Deng and Sakura [13] used GA to generate tradng rules based on a techncal ndcator for FX tradng. Hrabayash et al. [14] used a GA to generate rules for FX ntraday tradng by mnng features from several techncal ndcators. Esfahanpour and Mousav [15] useda GA to generate rsk-adjusted rules for tradng. In addton to GAs, dfferental evoluton (DE) was proposed by Storn and Prce [16] and t s a populaton based stochastc search, whch functons as an effcent global optmzer n contnuous search domans. DE has been appled successfully n varous felds. For example, Worasucheep [17] used DE for forecastng the stock exchange ndex of Thaland. Takahama et al. [18] used DE to optmze neural networks for predctng stock prces. Peralta et al. [19] compared DE and GA for tme seres predcton and showed that the performance of DE was better than GA f more than 150 generatons were generated. In addton to SVMs, n the last decade, many researchers haveusedthemultplekernellearnng(mkl)[20, 21] to address the problem of selectng sutable kernels for dfferent feature sets. Ths technque mtgates the rsk of erroneous kernel selecton to some degree by takng a set of kernels, dervng a weght for each kernel, and makng better predctons based on the weghted sum of the kernels. One of the major advantages of MKL s that t can combne dfferent kernels for varous nput features. Many researchers have appled MKL n ther research felds. For example, MKL was used by Joutou and Yana [22] for food mage recognton. Forest et al. [23] used MK regresson for wnd speed predcton and ther results outperformed those of several conventonal methods. Recently, researchers have used MKL for predctng the FX rate, crude ol prces, and stock prces. For example, Deng et al. [24] used MKL to fuse the nformaton from stock tme seres and socal network servce for stock prce predcton. Deng and Sakura [25]usedMKL for predcton and tradng on crude ol markets. Fletcher et al. [26] used MKL for predctng the FX market from the lmt order book. Luss and D Aspremont [27] employed MKL for predctng abnormal returns based on the news usng text classfcaton. Yeh et al. [28] used MKL to predct stock prces onthetawanstockmarketandtheyshowedthatmklwas better than SVM for evaluatng performances. Deng et al. [7] used MKL to predct short-term foregn exchange rate, and the predcton results of MKL based method are much better than conventonal methods, n terms of root mean square(rmse).thedfferencebetweenthemethodproposed n Deng et al. [7] and ths study s that the proposed method n ths study uses one MKL to predct upward trend and uses another MKL for predcton of downward trend, whle the method n Deng et al. [7] susedmklto predct the change rates of FX rate. The reason for usng one MKL to predct upward trend and usng another MKL topredctdownwardtrendsthatourclassfcatonsa three-classfcaton problem (upward trend, downward trend, and unknown). In addton, ths study uses one techncal ndcator (RSI) but from three dfferent tmeframes, whle Deng et al. [7] used three techncal ndcators but from one tmeframe. Deng et al. [7] used multple techncal ndcators because of the dfferences between dfferent techncal ndcators snce they may provde dfferent tradng sgnals, whlethsresearchusedmultpletmeframesofonetechncal ndcator snce dfferent tmeframes of the same techncal ndcator may provde dfferent tradng sgnals. In addton to usng ndvdual method, several researchers have used hybrd models for tradng stocks or FX rate predcton. For example, Huang and Wu [29] usedsvmandgantegrated model for predctng a stock ndex. Huang [30] combned SVM wth GA to produce a stock selecton model. The better performances of the hybrd SVM-GA model than ndvdual method (SVM or GA), the superorty of DE to GA [19], and superorty of MKL to SVM [22, 26, 28] nspredusto try a new hybrd model whch combnes MKL and DE. It s logcally expected that a MKL-DE wll perform better than the prevous methods. Inthepresentstudy,weuseahybrdmethodbasedon MKL and DE for predcton and to generate the tradng rules for tradng currency rates. In addton, we notced that some researchers focused on extreme returns or abnormal movements of stock prces. For example, Benesh et al. [31] used contextual fundamental analyss for stock predcton and they focused only on extreme returns, that s, returns above a threshold. Luss and D Aspremont [27] used MKL and they focused on abnormal movements, whch were movements above a threshold. Inspred by ther research, n ths study, we use MKL to generate sgnals for upward trends, downward trends, and no trend. The drectonal
The Scentfc World Journal 3 change predctor performs learnng to predct the drecton of prce movements. The drecton of movement s classfed as an upward trend, a downward trend, or a probablstc fluctuaton. Thus, we smply set a threshold for the absolute values of changes, below whch we consder the change to be afluctuaton. In addton to trends, traders also consder the possblty of overbought or oversold condtons for the target currency par. For example, f a trader predcts an upward trend but thetargetcurrencyparsoverbought,thats,atahgh level, t wll be rsky to contnue followng the trend. We could use a techncal ndcator as a tool to determne the degreetowhchthefxparsoversoldoroverbought,before generatng tradng actons (buy, sell, or no trade) based on the overbought or oversold sgnal. In ths study, we defne theoverboughtoroversoldsgnalsbasedonarsi(referto Secton 2.1.3). Our tradng tme horzon s 1 hour, whch means that we assess overbought or oversold sgnals based only on 1- hour tme frame data. Clearly, t s possble that the judgment would be dfferent f we made assessments usng a longer or shorter tmeframe. For example, Fgure 1 shows theeur/usdrateandtsrsivaluesfor1-hourand2- hour tmeframes (.e., 1-hour RSI and 2-hour RSI values). Note that at the eghth pont (10:00:00, May 5, 2011) n Fgure 1, the 1-hour RSI value s approxmately 73.90, whch provdes us wth a sell sgnal because the currency par s overbought, whereas the 2-hour RSI value s approxmately 43.98, whch tells us that the currency s not overbought. The rate ncreased further from the eghth to the nnth pont (11:00:00, May 5, 2011). In addton, the 1-hour RSI value s approxmately 78.32 at the nnth pont and the 2-hour RSI value s approxmately 71.71, whch suggests that both values provde overbought sgnals so t s hghly probable that the rate wll decrease from the nnth pont onwards. Ths example shows that f we use the RSI to generate tradng rules, we must assess the overbought or oversold condtons not only forthetargettmeframe,butalsoforrelatvelylongerand shorter tmeframes. For example, the features of the RSI from a relatvely shorter tmeframe (.e., 30 mnutes n ths study) and a relatvely longer tmeframe (.e., 2 hours) were used n ths study as sutable sgnals for tradng a target currency par. In the present study, we use the MACD ndcator of two currency pars as features, rather than only the target currency par, and the RSI ndcator from two dfferent tmeframes of the target tradng currency par, rather than the target tmeframe. Accordng to the 2010 Trennal Survey (the share of tradng volume), the most heavly traded currency pars were: EUR/USD 28%, USD/JPY 14%, and GBP/USD 9%. The EUR/USD s the most traded currency par n the world, so ths s used as our target tradng currency par. JPY and GBP are the two most hghly exchanged currences wth both USD and EUR, so we also employ GBP/USD and USD/JPY as supplementary nformaton for predctng our target currency par. Evaluatons of the expermental results should be based onthereturn-rskratoaswellasthereturnandtheaverage return, because most nvestors prefer to obtan stable returns, Rate Value Value 1.480 1.465 70 50 30 10 70 50 30 10 EUR/USD rate 2 4 6 8 10 12 14 Index RSI 1hour (parameter n=6) 2 4 6 8 10 12 14 Index RSI 2hour (parameter n=6) 2 4 6 8 10 12 14 Index Fgure 1: Example showng the relatve strength ndex values from multple tmeframes. rather than hgh returns wth hgh volatlty, that s, hgh rsk.therefore,thesharperato[32]susedasanevaluaton measuretoadjustthersk,naddtontotheaveragereturn. In summary, ths study makes three man nnovatons, as follows: (1) to predct drectonal changes of EUR/USD, we set thresholds on the magntude of the FX rate changes to dstngush upward trend or downward trend from random fluctuatons to predct the return, whereas only a few studes employed ths process. (2) To generate a trade sgnal, we fuse nformaton from multple currency pars other than only the target currency par and we combned multple RSIs from multple tmeframes other than only the target tradng tmeframe, whereas many prevous researchers have consdered only the target tradng currency par wth a target tradng tmeframe. (3) The hybrd model combned an upward trend/down ward trend sgnal wth the multple RSI sgnal, and the hybrd model yelded greater profts. Proposed model outperformed the baselne and other methods based on the results of return and the return-rsk rato. The remander of ths paper s organzed as follows. Secton 2 descrbes the background of ths research. Secton 3 explans the structure of the proposed method. Secton 4 descrbes the expermental desgn. Secton5 presents the expermental results and provdes a dscusson. Secton6 concludes the paper. 2. Background 2.1. Techncal Indcators. Techncal ndcators are broadly classfed nto two types: trend ndcators and oscllator ndcators. The best-known trend ndcator s the MA, whch s the bass of most other ndcators. Next, we ntroduce the three techncal ndcators used n ths study: MA, MACD as a trend ndcator, and RSI as an overbought/oversold ndcator.
4 The Scentfc World Journal 2.1.1. Smple MA and Exponental MA. The MA s a technque for smoothng out short-term fluctuatons, whch can be obtaned by calculatng the mean value of the prces over the past n-perods. The MA s used to understand the present trend, whch s why t s a so-called trend-followng ndex. There are several types of MA, dependng on how past prces are weghted. The smple MA (SMA) s a smple mean value wth dentcal weghts for past prces: SMA n (t) = t k=t n+1 P (k), (1) n where n stheperodlengthandp(k) s the foregn exchange rate or some other value under consderaton. Another type of MA, the exponental MA (EMA), s the mean of the underlyng data, whch s generally the prce of a stock or foregn exchange rate for a gven tme perod n, where larger weghts are attrbuted to narrower changes. The dfference between the EMA and the SMA s that the EMA s concerned more wth the nearest movements, whch may have greater effects on future changes than older changes. The EMAscalculatedasfollows: EMA n (t) =P(t) a+(1 a) EMA n (t 1), (2) where EMA n (t) s the EMA of the rate at tme t and a=2/(n+ 1),whch s commonlyused for the n-perod EMA. 2.1.2. MACD. The MACD s used to predct trends n tme seres data and t provdes two ndcators: the MACD value and the MACD sgnal. In general, the MACD value s the dfference between the 12-perod and 26-perod EMAs, as follows: MACD value (t) = EMA 12 (t) EMA 26 (t). (3) The MACD sgnal s equal to the 9-perod EMA of the MACD value, as follows: MACD sgnal (t) = EMA 9 (MACD value (t)). (4) The MACD parameters (12, 26, and 9) can be adjusted to meet the needs of traders. In our study, we smply use the default MACD parameters gven above because they are used wdely throughout the world. 2.1.3. RSI. In general, traders use the RSI as a momentum oscllator to compare the magntude of recent gans wth the magntude of recent losses. If we let P(t) represent the closng prceondayt, then we can calculate the gan or loss n perod t as follows: P (t) P(t 1) f P (t) >P(t 1) G t ={ 0 otherwse, P (t) P(t 1) f P (t) <P(t 1) L t ={ 0 otherwse. (5) Next, the n-perodaveragegan (AG(t))scalculatedas AG (t) = n 1 AG (t 1) + 1 n n G t, (6) and the n-perod average loss (AL(t))scalculatedas AL (t) = n 1 AL (t 1) + 1 n n L t. (7) Thus, the n-perod RSI at tme pont t s calculated as AG (t) RSI n (t) = 100. (8) AG (t) + AL (t) Tradtonally, a RSI value hgher than 70 ndcates that the currency has been overbought, whereas a value below 30 ndcates that the currency par has been oversold. Thus, the RSI provdes alarm sgnals for nvestors to close the current poston or to open a new poston to buy when the currency soversoldandtosellwhentsoverbought.theparameters used for the overbought and oversold levels can be set up by traders. In the present study, we use DE to optmze the RSI parameter. 2.2. SVM and MKL. A SVM s an optmal hyperplane used to separate two classes or a nonlnear separatng surface optmzed usng a nonlnear mappng from the orgnal nput space nto a hgh-dmensonal feature space to search for an optmally separatng hyperplane n the feature space. The latter solves classfcaton problems that cannot be lnearly separated n the nput space. We desgnate a hyperplane as optmal f t has a maxmal margn, where the margn s the mnmal dstance from the separatng hyperplane to the closest data ponts, whch are called the support vectors. The concept used to map the data from the orgnal feature space to a hgh-dmensonal feature space s called a kernel method. Fndng the optmal hyperplane s formalzed as follows: mn n ζ =1 1 2 w 2 +C s.t. y ( w x +b) 1 ζ, ζ 0, =1,2,...,n, where w s the vector of the parameters that defne the optmal decson hyperplane w x +b = 0and b represents the bas. (1/2) w 2 s consdered to be a regularzaton term, whch controls the generalzaton capactes of the classfer. The second term C n =1 ζ s the emprcal rsk (error). C s sometmes referred to as the soft margn parameter and t determnes the tradeoff between the emprcal rsk and the regularzaton term. Increasng the value of C gves greater mportance to emprcal rsk relatve to the regularzaton term. Postve slack varables ζ allow classfcaton errors. To extend SVM, MKL uses multple kernels to map thenputspacetoahgher-dmensonalfeaturespaceby combnng dfferent kernels to obtan a better separaton functon. In MKL, the kernels are combned lnearly and the (9)
The Scentfc World Journal 5 weght of each kernel reflects ts mportance. The kernels can be dfferent kernels or the same kernels wth dfferent parameters. Each kernel n the combnaton may account for a dfferent feature or a dfferent set of features. The use of multple kernels can enhance the performance of the model. Suppose k m (m = 1,...,M) are M postve defnte kernels on the same nput space. Fndng the optmal decson surfacesformalzedasfollows: mn w,b,ζ 1 2 M m=1 1 d F m 2 H m +C m M N n ζ =1 =1 X 2, s.t. y ( F m,φ m (x ) + b) 1 ζ, M m=1 m=1 ζ 0, d m =1, d m 0, =1,2,...,n, (10) where Φ s a possbly nonlnear mappng from the nput space to a feature space, F m s the separaton functon, s anorm,, s the nner product, C s used to control the generalzaton capactes of the classfer, whch s selected by crossvaldaton, and d m are the optmzed weghts. In our study, the optmzed weghts d m drectly represent therankedrelevanceofeachfeatureusednthepredcton process. We employ MKL to learn the coeffcents and parameter of the subkernels. We used the multple kernel learnng toolbox SHOGUN[21] n our experments. In our MKL based models, smlarty s measured based on the nstances of EUR/USD, nstances of USD/JPY, and nstancesofgbp/usd.weconstructthreesmlartymatrces for each data source. These three derved smlarty matrcesarealsotakenasthreesubkernelsofmklandthe weghts of d m,eurusd, d m,gbpusd,andd m,usdjpy are learnt for the subkernels: k( x, x j )=d m,eurusd k EURUSD ( x (1) +d m,gbpusd k GBPUSD ( +d m,usdjpy k USDJPY (, x (1) j ) x (2) x (3), x (2) j ), x (3) j ), (11) where x, = 1,2,...,n,aretranngsamples,d m,eurusd, d m,gbpusd,andd m,usdjpy 0,andd m,eurusd +d m,gbpusd + d m,usdjpy = 1. x (1) are EUR/USD nstances, x (2) are GBP/USD nstances, and x (3) are USD/JPY nstances. In ths study, k s the RBF (radal bass functon) kernel for SVMandMKL.Forothertypesofnformatonsourcesor subkernel combnatons, smlar dstance based smlarty matrces and kernel functons can be constructed, whch are easly mported nto our multkernel based learnng framework. doman. Lke other evolutonary algorthms, DE also has a populaton wth the sze N p and D-dmensonal parameter vectors (D s the number of parameters present n an objectve functon). Two other parameters used n DE are the scalng factor F and the crossover rate C r. 2.3.1. Populaton Structure. The current populaton, represented by P x, comprses the vectors x (G), whch have already been found to be acceptable, ether as ntal ponts or based on comparsons wth other vectors, as follows: P (G) x x (G) = (x (G) ) =0,1,...,N P 1, G=0,1,...,g max, = (x (G),j ) j=0,1,...,d 1. (12) After ntalzaton, DE mutates randomly selected vectors to produce an ntermedary populaton P (G) V of N p mutant vectors V (G). Consder P (G) V V (G) = (V (G) ) =0,1,...,N P 1, G=0,1,...,g max, = (V (G),j ) j=0,1,...,d 1. (13) Each vector n the current populaton s recombned wth amutanttoproduceatralpopulatonp u of N p tral vectors u (G). Consder P (G) u u (G) = (u (G) ) =0,1,...,N P 1, G=0,1,...,g max, = (u (G),j ) j=0,1,...,d 1. (14) 2.3.2. Intalzaton. Before the populaton can be ntalzed, theupperandlowerboundsofeachparametermustbe specfed. They can be collected nto two D-dmensonal ntalzaton vectors, x U and x L.Afterthentalzatonbounds have been specfed, a random number generator assgns each element of every vector wth a value from the prescrbed range. For example, the ntal value (G = 0) of the jth parameter of the th vector s P (0) =x (0),j =x j,l + rand j [0, 1] (x j,u x j,l ) =0,1,...,N P 1; j=0,1,...,d 1, (15) where rand j [0, 1] s a random number, whch s generated unformly between 0 and 1. 2.3.3. Mutaton. After ntalzaton, DE mutates and recombnes the populaton to produce a populaton of N p tral vectors. A mutant vector s produced accordng to the followng formulaton: 2.3. DE. The DE method proposed by Storn and Prce [16]s a populaton based stochastc search approach, whch can be used as an effcent global optmzer n a contnuous search V (G),j =x (G 1) r1,j =0,1,...,N P 1; +F (x (G 1) r2,j x (G 1) r3,j ) j=0,1,...,d 1. (16)
6 The Scentfc World Journal The scale factor F s a postve real number, whch controls therateofpopulatonevoluton.theresnoupperlmttof, buteffectvevaluesareseldomgreaterthan1. r1, r2, andr3 refer to three randomly selected ndces from the populaton. 2.3.4. Crossover. DE also employs unform crossover. Sometmes referred to as dscrete recombnaton, crossover bulds tral vectors from elements that have been coped from two dfferent vectors. In partcular, DE crosses each vector wth a mutant vector: u (G) { V (G),j f (rand (G),j C r or j=j rand ),j = { x (G 1) (17),j otherwse, { where the crossover probablty C r [0, 1] s a user-defned value, whch controls the fracton of elements that are coped from the mutant. To determne the source that contrbutes, a gven unform crossover compares C r to a unform random number rand (G),j between 0 and 1. If the random number s less than or equal to C r, the tral element s nherted from the mutant V (G) ; otherwse the element s coped from the vector x (G 1). In addton, the tral element wth the randomly selected ndex j rand s taken from the mutant to ensure that the tral vector does not duplcate x (G). 2.3.5. Selecton. If the tral vector u (G) has an equal or lower objectve functon value than that of ts target vector x (G),t replaces the target vector n the next generaton; otherwse the target retans ts place n the populaton for at least one more generaton: x (G+1) ={ u(g) x (G) f f(u (G) ) f(x (G) otherwse. ) (18) 2.3.6. Stoppng Crtera. After the new populaton s generated, the processes of mutaton, recombnaton, and selecton are repeated untl the optmum s obtaned, or a user-defned termnaton crteron, such as the number of generatons, s reached at a preset maxmum g max. 2.4. Evaluaton Measures. In the present study, we performed smulated tradng usng test samples based on the tradng sgnals generated by MKL predcton and the multple RSI sgnal, and we evaluated the return (gan or loss) obtaned wth the proposed model and other models. In general, a hgh return s nevtably accompaned by the potental for hgh rsk. Therefore, nvestors desre a method that decreases rsk whlenotdecreasngtheproftsgreatly,whchresultsna trade-off relatonshp. The Sharpe rato, named after Wllam Forsyth Sharpe, s a measure of the excess return per unt of rsk n an nvestment asset or a tradng strategy, whch s defned as follows: S= E[R R f] σ = E[R R f], (19) var [R R f ] where R s the asset return, R f s the return on a benchmark asset (usually a very low rsk return such as a three-month US treasury bll), σ s the standard devaton of the asset return, and E[R R f ] s the expected value of the excess of the asset return relatve to the benchmark asset return [32]. In our experments, we used the Sharpe rato as an evaluaton measure to assess the return-rsk rato performance of our proposed method wth other methods. 3. Proposed Method 3.1. Structure of the Proposed Method. Fgure 2 shows the structure of the proposed method. Frst, the proposed method uses a MKL framework to predct drectonal changesnthecurrencyratebasedonthemacdofthree currency pars. The RSI sgnals are generated usng multple tmeframe features of EUR/USD by consderng the MKL tradng sgnals. Fnally, the MKL sgnal and RSIs sgnal are combned to produce a fnal decson, that s, the tradng sgnal. The predcton and tradng target currency par n ths study s EUR/USD. We selected t as our target due to the fact that the euro and US dollar are the two most traded currences n the world, representng the world s two largest economes. Therefore, to better predct the changes n EUR/USD s consdered to contrbute much to the nvestors and nternatonal companes. In addton to EUR/USD data tself, snce the two most traded currences wth USD and EUR n FX market are JPY and GBP, USD/JPY and GBP/USD are used for EUR/USD predcton. These three currency pars share almost 50% of the FX market; other currences such as AUD (Australan dollars), CAD (Canada dollars), and CHF (Swss Franc) are also mportant currences but snce ther shares n FX market are relatvely small, we dd not consder them n the structure of the proposed method. The tradng tme nterval s selected to be one hour n ths study, whch s also selected by Hrabayash et al. [14]. To fnd overbought/oversold ndcator values other than target 1-hour horzon data and to select some reasonable longer and shorter tme horzons data are mportant. Snce the tradng tme nterval s one hour, 30-mnute and 2-hour tme horzon data are consdered to be useful. Too hgh frequency tme horzon data (such as mnute data) or too low frequency tme horzon data (such as daly data) are consdered to have small mpact f we fx the tradng tme nterval to be one hour. In ths proposed method, we use MKL to predct drectonal changes and DE to fnd overbought/oversold nformaton from RSI ndcator. Although the predcted drectonal change can be used for smulated tradng, n our prelmnary experments, the accumulated profts based on just the MKL predctons were not good enough (refer to Secton 5.1); the samewastrueforaccumulatedproftsbasedonusngjustde and RSI ndcator. Consderng that the predcton and the techncal ndcators mght have complementary components, we propose to combne them to get the tradng sgnal. Therefore,wecombneMKLandDEntheproposedmethod. 3.2. MKL Input and Output. For MKL, the nput features are derved from three dfferent sources: EUR/USD, GBP/USD,
The Scentfc World Journal 7 Multple kernel learnng GBP/USD 1-hour MACD Sgnal MKL USD/JPY 1-hour MACD MKL up-trend classfer MKL down-trend classfer Combnaton 1 Combned tradng sgnal EURUSD 1-hour MACD MKL sgnal Combnaton 2 30-mn RSI Tradng sgnal 1-hours RSI Weghted sum RSIs sgnal 2-hours RSI Sgnal RSIs Dfferental evoluton Fgure 2: Structure of the proposed method. Table 1: Features for each kernel. No. Feature 1 MACD-value at tme t 2 MACD-sgnalattmet 3 MACD-value at tme (t 1) 4 MACD-sgnalattme(t 1) 5 MACD-value at tme (t 2) 6 MACD-sgnalattme(t 2) 7 MACD-value at tme (t 3) 8 MACD-sgnalattme(t 3) 9 MACD-value at tme (t 4) 10 MACD-sgnal at tme (t 4) 11 MACD-value at tme (t 5) 12 MACD-sgnal at tme (t 5) 13 MACD-value at tme (t 6) 14 MACD-sgnal at tme (t 6) 15 MACD-value at tme (t 7) 16 MACD-sgnal at tme (t 7) andusd/jpy.wetransformtheratestomacdsgnalsand values. For each kernel, the nputs are the MACD values and MACD sgnals for eght consecutve perods, whch are shown n Table 1. Usng MKL, we construct two classfers to output the MKL-up labels and the MKL-down labels (MKL-up refers to an upward trend classfer learned by MKL, whle MKLdown refers to a downward trend classfer learned by MKL). We want to predct drectonal changes n a currency wth an nsenstve nterval, where the changes from 0.1% to 0.1% are not consdered upward or downward. Thus, we set two threshold values, that s, 0.1% and 0.1%, whch we refer to as the uptrend threshold value and the downtrend value, respectvely, to label the tranng and testng samples. The rules for the MKL-up trend and MKL-down trend classfers are shown n Table 2. BasedonthepredctonsofthesetwoMKLclassfers,we obtanacombnedmklsgnalbasedontherules,whchare shown n Table 3. The combned MKL tradng sgnal s one of the nputs for DE that needs to be combned wth the multple RSI sgnal. 3.3. Combned Tradng Sgnal Based on the Combned MKL and Multple RSI Sgnals. The multple RSI sgnal value Value RSIs sthecombnedvalueofthreetmeframersivalues: Value RSIs = 3 =1 w e, (20) where w are the weghts of the three RSIs and e s the value of the RSI ndcator. Note that the value of the RSI ndcator s expressed as a rato and we use RSI/100 from (8). The weghts w ofeachrsiarelearnedbyde. We compare the RSI values n (20) wththebuy/sell thresholdtodetermnethemultplersisgnal.thesgnaland the condton that need to be satsfed before the sgnal can be ssued are shown n Table 4. Sgnal tradng s a sgnal used for makng decsons based on both the combned MKL sgnal and the multple RSI sgnal. Table 5 shows how the combned MKL and multple RSI sgnal are combned to obtan the tradng sgnal. If we decde to take a poston (buy or sell), the poston s retaned
8 The Scentfc World Journal Table 2: Output labels for MKL up-trend and down-trend classfers. MKL classfer MKL-trend sgnal Condtons MKL-up trend MKL-up = +1 If the actual change rate s greater than the upward trend threshold value MKL-up = 1 If the actual change rate s less than the upward trend threshold value MKL-down trend MKL-down = +1 If the actual change rate s less than the downward trend threshold value MKL-down = 1 If the actual change rate s greater than the downward trend threshold value Table 3: Condtons for ssung the MKL sgnal. No Combned MKL sgnal (Sgnal MKL ) Condtons 1 No trade MKL-up = 1 and MKL-down = 1 2 No trade MKL-up = 1 and MKL-down = 1 3 Buy MKL-up = 1 and MKL-down = 1 4 Sell MKL-up = 1andMKL-down=1 Table 4: Condtons that need to be satsfed before ssung the RSI sgnal. No Multple RSI sgnal (Sgnal RSIs ) Condtons 1 Buy Value RSIs < buy threshold 2 Sell Value RSIs > sell threshold 3 No trade otherwse Table 5: Condtons that need to be satsfed before ssung the tradng sgnal. Tradng sgnal (Sgnal tradng ) Combned MKL sgnal (Sgnal MKL ) Condtons Multple RSI sgnal (Sgnal RSIs ) Buy Buy No trade Sell Sell No trade No trade No trade No trade Sell Any (buy, sell, or no trade) Sell Buy Any (buy, sell, or no trade) Buy for 1 hour; that s, we check the condtons every hour. If the tradng sgnal (buy or sell) s the same as that 1 hour before, we do not trade and we wat for 1 hour. The data we use are 1- hour EUR/USD (we used 30 mn data to calculate the 30 mn RSIvalue,and1-hourdatatocalculatethe1-hourRSIvalue and the 2-hour RSI value). 3.4. DE Parameter Desgn. The DE parameter vectors shown n Table 6 areusedtoconstructthemultplersisgnals.the representatons of the parameter vectors are as follows. (1) The frst three groups represent the parameters for eachrsi(threersisntotal).thevaluesrangefrom 3to10(ntegertype). (2)Numbers4to5areusedtodecdethetmestobuy, sell, and close postons. The values range from 0 to 2 (floatng pont number type). Table 6: DE parameter vector desgn. No Value Descrpton 1 3 to 10 parameter for 1-hour RSI 2 3 to 10 parameter for 2-hour RSI 3 3 to 10 parameter for 30-mn RSI 4 0 to 2 buy threshold 5 0 to 2 sell threshold 6 0to1 weghtvaluefor1-hourrsi 7 0to1 weghtvaluefor2-hourrsi 8 0 to 1 weght value for 30-mn RSI (3)Numbers6to8aretheweghtsusedtolnearly combne sgnals, whch are descrbed n (20) n Secton 3.3. The values range from 0 to 1 (floatng pont number type). The populaton sze s set to 200 and the maxmum number of generatons s set to 200 durng the DE tranng step. The accumulated return obtaned n the tranng step s selected as the objectve functon. 4. Experment Desgn The exchange rates used n ths study were obtaned from ICAP. The ICAP data was used n our prevous study [13]for tradngoneur/usd.theicapdatausethegmt+1hour tme zone (GMT +2 hour n summer) and they do cover the exchange rate n weekend. A lst of best offers, best bds, and dealt prces for every second are comprsed n the ICAP data. We transformed them nto 30 mn and 1-hour tmeframes. We used exchange rate data for three currency pars from ICAP data: EUR/USD, GBP/USD, and USD/JPY. We separate the overall data nto three datasets and each dataset covered the perod from January 3 to December 30 n each year, wth a total of about 6200 observatons (hourly data). The three datasets used for tranng and testng are shown n Table 7. Thedatancludethe open,hgh,low,andclose rates durng each tme nterval (30 mn and 1 hour). The data were dvded nto three dsjont datasets that covered consecutve perods, the detals of whch are shown n Table 8. Next, we dvded each dataset nto a tranng perod and a testng perod.themkltranngperodcovered3000observatons (around 6 months) and the testng perod covered 3000 observatons (around 6 months). The MKL-DE tranng step covered 1500 tradng hours and the MKL-DE testng step covered 1500 tradng hours. Detals of the length of each perodareshownntable 8.
The Scentfc World Journal 9 Table 7: Three datasets used for tranng and testng. Dataset MKL tranng MKL testng MKL-DE tranng MKL-DE testng Dataset 1 (2008) Jan. to Jun. Jul. to Dec. Jul. to Sep. Oct. to Dec. Dataset 2 (2009) Jan. to Jun. Jul. to Dec. Jul. to Sep. Oct. to Dec. Dataset 3 (2010) Jan. to Jun. Jul. to Dec. Jul. to Sep. Oct. to Dec. Table 8: Tradng and testng perods for MKL and DE. Perod Process Length of perod 1 MKL learnng 3000 tradng hours (around 6 months) 2 MKL testng (predcton) 3000 tradng hours (around 6 months) 2-1 MKL-DE tranng 1500 tradng hours (around 3 months) 2-2 MKL-DE testng (tradng) 1500 tradng hours (around 3 months) Foregn exchange market s often and suddenly affected by economc events such as a bank rate decson or even unpredctable affar such as a bg earthquake. Therefore, n a tradng n the experments, our ntal nvestment s A US dollars. For each transacton (long or short), we fx the tradng amount to be A/2 US dollars wth a tradng leverage rato of 2 to 1. That s, although we dd margn transacton, the tradng n our experments s conducted wth very low leverage (or wthaveryhghmargnlevel),whchensuresthesafetyof our transacton order even though there s a bg shock n FX market. Table 9 shows a lst of the methods tested, ncludng baselne methods, proposed methods, and ntermedate methods. Buy and hold and sell and hold were selected as baselne methods because they are smple and well known, whle they are the best methods for obtanng zero proft on average f the market s effcent and statonary. The tradng rule they used was to buy or sell at the start of the testng perod and to close the poston at the end of the testng perod. The other methods used for comparson comprsng the smplest methods and our proposed methods. SVM-s used a kernelzed lnear model for exchange rates where the nputs were the exchange rates of only one currency par wth SVM as a learnng method. SVM-m was the same as SVM-s but t utlzed the features of three currency pars. MKL-m was the same as SVM-m but the model was a multple kernelzed lnear model that uses MKL. MKL-m-t and MKL-m-t-DE werethesameasmkl-mbutthepredctonwaschanged to a three-classfcaton problem from a two-classfcaton problem. The tradng rule used by SVM-s, SVM-m, and MKL-m was to buy a currency par when the predcton was postve, to sell when negatve, and no trade when the predcton was 0. The tradng rule for MKL-m-t was based on Sgnal MKL. The tradng rule used by MKL-m-t-DE, our proposed method, was based on Sgnal tradng where the parameters were optmzed usng MKL and DE (see Table 5). DE-only was based on Sgnal RSIs ; that s, t reled only on multplersisgnals.thedealgorthmncludesrandom numbers, so we conducted 10 experments wth dfferent seeds for MKL-m-t-DE and DE-only. In the lst of methods tested, snce GA based method are well-known methods n the prevous lteratures [12 14], GA-s and GA-m whch are mplemented by Deng and Sakura [13] are consdered as benchmark methods, and we conducted 10 experments wth dfferent seeds for GA-s and GA-m. Buy and hold and sell and hold are well-known baselne methods whch are also used as baselne methods by Chong and Ng [9]; SVM-s, SVM-m, MKL-m, MKL-m-t, DE-only, and MKL-m-t-DE are mplemented by us. 5. Expermental Results and Dscusson 5.1. Returns wth the Three Datasets. Table 10 shows the returns wth the methods tested, where the returns were measured n proporton to the ntal nvestment (the entres n the frst three columns for MKL-m-t-DE, DE-only, GAs, and GA-m are the average returns from 10 ndependent experments wth ther standard devatons). Frst, we found that durng the testng perod (three months) for each dataset, our proposed method yelded good average returns (about 6.73%, 4.71%, and 3.52%). In addton, our proposed method obtaned the best average return (4.98%) among all the methods tested. Next,wefocusedonthebaselnemethods: buyand hold and sell and hold. We found that buy and hold yelded losses wth all three testng datasets whle sell and hold yelded better returns than the other methods except MKL-m-t-DE durng the three testng perods. The sell and hold strategy yelded profts durng the testng perods because EUR had declned aganst USD due to the European soveregn debt crss [33], whch occurred n the Eurozone after a bg rse n EUR aganst USD from 2005 untl the frst half of 2008. We could not forecast the declne or surge before thsperod,sowecouldnotdecdewhether buyandhold wasbetterthan sellandhold andwecouldnotconcludethat these two naïve strateges performed well. In addton, we compared the results wth SVM-s and SVM-m. Table 10 shows that these SVM based methods yelded losses durng all three testng perods. SVM-m used more nformaton (the features of three FX pars) than SVMs (the features of EUR/USD only) n dataset 2 (2009), but the
10 The Scentfc World Journal Table 9: Lst of the methods tested. Method GA-s GA-m Buy and hold Sell and hold SVM-s SVM-m MKL-m MKL-m-t DE-only MKL-m-t-DE Descrpton Trade based on the tradng rules optmzed by GA, wth one RSI nput Trade based on the tradng rules optmzaton by GA, wth three RSI nput Buy and hold untl the end pont of a perod Sell and hold untl the end pont of a perod Trade based on SVM predcton, wth one FX par nput Trade based on SVM predcton, wth three FX pars nput Trade based on MKL predcton, wth three FX pars nput Trade based on Sgnal MKL Trade based on Sgnal RSIs (parameters are optmzed by DE) Trade based on Sgnal tradng Table 10: Returns wth the methods tested (The numbers rght to ± s the standard devaton). Method Dataset 1 (2008) Dataset 2 (2009) Dataset 3 (2010) Average returns GA-s 0.0068 ± 0.0230 0.0454 ± 0.0143 0.0284 ± 0.0569 0.0223 GA-m 0.0098 ± 0.0991 0.0326 ± 0.0286 0.0087 ± 0.0241 0.0046 Buy and hold 0.0510 0.0426 0.0229 0.0388 Sell and hold 0.0510 0.0426 0.0229 0.0388 SVM-s 0.2039 0.0225 0.0559 0.0941 SVM-m 0.0397 0.0324 0.0299 0.0340 MKL-m 0.1932 0.0103 0.0479 0.0518 MKL-m-t 0.0216 0.0150 0.0048 0.0138 DE-only 0.0035 ± 0.0991 0.0318 ± 0.0541 0.0082 ± 0.0131 0.0201 MKL-m-t-DE 0.0673 ± 0.0343 0.0471 ± 0.0362 0.0352 ± 0.0215 0.0498 return wth SVM-m ( 3.2%) was not better than that wth SVM-s ( 2.2%). Moreover, we compared the results of proposed method wth that of GA-s and GA-m. Table 10 shows that GA-s yelded postve return on average durng 2008, whle yelded losses on average durng 2009 and 2010. GA-m yelded postve return n 2008 and 2010, but t yelded losses on average durng 2009 and the average return of three data sets s about 0.004, whch s much worse than the results of our proposed method. In addton, the average return results of GA-m for the three data sets are better than those of GA-s, whch agrees wth the concluson n Deng and Sakura [13] that the return results mproved when usng nformaton of RSI ndcator from multple tmeframes. Basedontheaveragereturns,wefoundthatMKL-m-t performed better than MKL-m, whch ndcated that the returns were mproved by neglectng small predcted changes such as fluctuatons n the MKL-m method. DE-only used DE alone to generate the tradng rules based on multple RSI values, but t yelded losses on average. MKL-m-t-DE performed the best of the four methods (MKL-m, MKL-m-t, MKL-m-t-DE, and DE-only), whch ndcates that the ntegratonofmultplersisgnalscouldmprovethetradngperformance. 5.2. Sharpe Ratos. In addton to the returns, the Sharpe rato was used to evaluate the performance of our proposed method and other methods. We used the one-year treasury rateasthersk-freeassettocalculatethesharperato.the one-year treasury rate ranged from 1.7% to 4.3% between 2008 and 2010. Next, we calculated the average rsk-free returns from 2008 to 2010 and the average rsk-free return for each testng perod (three months n each year) was about 0.75%. Table 11 shows the average returns, standard devatons,andsharperatoswtheachmethod(forthemethods MKL-m-t-DE and DE-only, average return results are the averages of all the returns obtaned from 10 experments for all the testng perods wth all the datasets, whle the standard devaton s the standard devaton of these returns). A hgher Sharpe rato ndcates a hgher return or lower volatlty. From Table 11, we found that for the methods GAs, GA-m, buy and hold, SVM-s, SVM-m, MKL-m, and DE-only, ther Sharpe rato values are negatve, whch ndcates that ther average return s less than the free-rsk asset. There are three methods that obtaned postve Sharpe rato value: sell and hold, MKL-m-t, and our proposed method MKL-m-t-DE. It s clear that our proposed method had a sgnfcantly hgher Sharpe rato (2.6111) than the other two methods durng the testng perods. The Sharpe rato results ndcate that the proposed method s the best method when evaluated by return-rsk rato. 6. Concluson and Future Work In ths study, we developed a hybrd method based on MKL and DE for EUR/USD tradng. In the frst step of our
The Scentfc World Journal 11 Table 11: Sharpe ratos for the baselne, benchmark, and proposed methods. Method Average return Standard devaton Sharpe rato GA-s 0.0223 0.0242 0.5025 GA-m 0.0046 0.0266 1.1177 Buy and Hold 0.0388 0.0144 3.2152 Sell and Hold 0.0388 0.0144 2.1736 SVM-s 0.0941 0.0965 1.0528 SVM-m 0.0340 0.0050 8.3000 MKL-m 0.0518 0.1258 0.4713 MKL-m-t 0.0138 0.0084 0.7500 DE-only 0.0201 0.0219 1.2602 MKL-m-t-DE 0.0498 0.0162 2.6111 approach, we used MKL to predct the drectonal change n the currency rate (wth an nsenstve nterval) to provde a combned MKL sgnal. In the second step, DE combned the combned MKL sgnal wth the multple RSI sgnal to generate a tradng sgnal. The expermental results showed that MKL-m-t yelded profts wth the three testng datasets (about1.38%onaverage),whlentegratonofthemultple RSI sgnal mproved the tradng profts (about 4.98% on average). In addton, the proposed method yelded the best Sharpe rato (about 2.61) compared wth all the models tested, whch ndcates that our proposed method outperformed other methods n terms of the return-rsk rato, as well as the returns. However, there are stll some unaddressed questons and some research drectons for future work. For example, how to fnd the best nsenstve nternal ( 0.1% to 0.1% n ths study) s stll an open queston n ths study: a too large nsenstve nterval could decrease the number tradng tmes toomuchsothatthetradngproftalsodecreases,whle a too small nsenstve nterval cannot flter the unknown movements well the tradng proft decreases. For future work, onemaycombnemklwthgatousegatosearchthebest parameters for nsenstve nterval n MKL automatcally n order to solve the unaddressed problems. In addton, other than RSI, some other famous overbought/oversold ndcators, such as BIAS and Wllam %R, could be also mplemented to mprove the tradng ablty. Conflct of Interests The authors declare that there s no conflct of nterests regardng the publcaton of ths paper. Acknowledgments Ths research was partally supported by the Graduate School Doctoral Student Grant-n-Ad Program 2012 of Keo Unversty, Japan. In addton, the authors wsh to thank ICAP for makng the data avalable for ths research. References [1] Onlne materal 1, Movng average, http://en.wkpeda.org/ wk/movng average. [2] Onlne materal 2, MACD, Wkpeda, http://en.wkpeda.org/wk/macd. [3] Onlne materal 3, RSI, Wkpeda, http://en.wkpeda.org/ wk/relatve Strength Index. [4] Onlne materal 5, BIAS rato, Wkpeda, http://en.wkpeda.org/wk/bas rato %28fnance%29. [5] Onlne materal 6, Bollnger Bands, Wkpeda, http://en.wkpeda.org/wk/bollnger Bands. [6] M. Jaruszewcz and J. Mańdzuk, One day predcton of NIKKEI ndex consderng nformaton from other stock markets, n Proceedngs of the 7th Internatonal Conference on Artfcal Intellgence and Soft Computng (ICAISC 04), pp. 1130 1135, Sprnger, Berln, Germany, June 2004. [7] S. Deng, K. Yoshyama, T. Mtsubuch, and A. Sakura, Hybrd method of multple kernel learnng and genetc algorthm for forecastng short-term foregn exchange rates, Computatonal Economcs,pp.1 41,2013. [8]L.Y.We,T.L.Chen,andT.H.Ho, Ahybrdmodelbased on adaptve-network-based fuzzy nference system to forecast Tawan stock market, Expert Systems wth Applcatons,vol.38, no. 11, pp. 13625 13631, 2011. [9] T. T.-L. Chong and W.-K. Ng, Techncal analyss and the London stock exchange: testng the MACD and RSI rules usng the FT30, Appled Economcs Letters, vol. 15, no. 14, pp. 1111 1114, 2008. [10] J. Kamruzzaman, R. A. Sarker, and I. Ahmad, SVM based models for predctng foregn currency exchange rates, n Proceedngs of the 3rd IEEE Internatonal Conference on Data Mnng (ICDM 03), pp. 557 560, Melbourne, Fla, USA, November 2003. [11] K. Shoda, S. Deng, and A. Sakura, Predcton of foregn exchange market states wth support vector machne, n Proceedngs of the 10th Internatonal Conference on Machne Learnng and Applcatons (ICMLA 11), vol. 1, pp. 327 332, Honolulu, Hawa, USA, December 2011. [12] Y. Chang Chen and Y. Chen, Mnng assocatve classfcaton rules wth stock tradng data-a GA-based method, Knowledge- Based Systems,vol.23,no.6,pp.605 614,2010.
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