ANN-Based Forecasting of Foreign Currency Exchange Rates

Transcription

1 Neural Informaion Processing - Leers an Reviews Vol. 3, No. 2, May 2004 LETTER ANN-Base Forecasing of Foreign Currency Exchange Raes Joarer Kamruzzaman Gippslan School of Compuing an Informaion Technology Monash Universiy, Churchill, Vicoria-3842, Ausralia Joarer Kamruzzama@inforach.monash.eu.au Ruhul A. Sarer School of Informaion Technology an Elecrical Engineering Universiy of NSW, ADFA Campus, NorhCo Drive, Canberra 2600, Ausralia ruhul@cs.afa.eu.au (Submie on March 24, 2004) Absrac - In his paper, we have invesigae arificial neural newors base preicion moeling of foreign currency raes using hree learning algorihms, namely, Sanar Bacpropagaion (SBP), Scale Conjugae Graien (SCG) an Bacpropagaion wih Bayesian Regularizaion (BPR). The moels were raine from hisorical aa using five echnical inicaors o preic six currency raes agains Ausralian ollar. The forecasing performance of he moels was evaluae using a number of wiely use saisical merics an compare. Resuls show ha significanly close preicion can be mae using simple echnical inicaors wihou exensive nowlege of mare aa. Among he hree moels, SCG base moel ouperforms oher moels when measure on wo commonly use merics an aains comparable resuls wih BPR base moel on oher hree merics. The effec of newor archiecure on he performance of he forecasing moel is also presene. Fuure research irecion oulining furher improvemen of he moel is iscusse. Keywors-Neural newor, ARIMA, financial forecasing, foreign exchange. Inroucion In he pas, foreign exchange raes were only eermine by he balance of paymens. The balance of paymens was merely a way of lising receips an paymens in inernaional ransacions for a counry. Paymens involve a supply of he omesic currency an a eman for foreign currencies. Receips involve a eman for he omesic currency an a supply of foreign currencies. The balance was eermine mainly by he impor an expor of goos. Thus, he preicion of he exchange raes was no a complex issue in he pas. Unforunaely, he ineres raes, an local an inernaional supply-eman facors ha become more relevan o each currency laer on. On he op of his, he fixe foreign exchange raes were abanone an a floaing exchange rae sysem was implemene by he inusrialize naions in 973. Recenly, furher liberalizaion of raes is being iscusse in General Agreemen on Trae an Tariffs. Due o he inroucion of floaing exchange raes an he rapi expansion of global raing mares over he las few ecaes, he foreign currency exchange mare has experience unpreceene growh. In fac, he exchange raes play an imporan role in conrolling ynamics of he exchange mare as well as he raing of goos in he impor-expor mares. For example, if he Ausralian currency is weaer han he US currency, he US raers woul prefer o impor cerain Ausralian goos, an he Ausralian proucers an raers woul fin he US as an aracive expor mare. On he oher han, if Ausralia is epenen on US for imporing cerain goos, i will hen be oo cosly for he Ausralian consumers uner he curren exchange raes. In ha case, Ausralia may loo for a beer source ha means shifing from he US o a new impor mare. As we can imagine, he rae relaion an he cos of expor/impor goos is irecly epenen on he currency exchange rae of he raing parners. The uraion of any inernaional rae agreemen beween any wo parners coul vary from shor erm o many years. However, he exchange raes vary coninuously uring he raing hours. As a resul, he appropriae preicion of exchange rae is a crucial facor for he success of many businesses an 49

2 ANN-Base Forecasing of Foreign Currency Exchange Rae J. Kamruzzaman an R. Sarer financial insiuions. Alhough he mare is well-nown for is unpreicabiliy an volailiy, here exis a number of ineres groups for preicing exchange raes using numerous convenional an moern echniques. Exchange raes preicion is one of he challenging applicaions of moern ime series forecasing. The raes are inherenly noisy, non-saionary an chaoic [5, 27]. These characerisics sugges ha here is no complee informaion ha coul be obaine from he pas behaviour of such mares o fully capure he epenency beween he fuure exchange raes an ha of he pas. One general assumpion is mae in such cases is ha he hisorical aa incorporae all hose behaviour. As a resul, he hisorical aa is he major player in he preicion process. Alhough he well-nown convenional forecasing echniques provie preicions, for many sable forecasing sysems, of accepable qualiy, hese echniques seem inappropriae for non-saionary an chaoic sysem such as currency exchange raes, ineres raes an share prices. The purpose of his paper is o invesigae he use of arificial neural newors base echniques for preicion of foreign currency exchange raes. We planne o experimen wih hree ifferen algorihms uner ifferen archiecure for several ifferen exchange raes. For more han wo ecaes, Box an Jenins Auo-Regressive Inegrae Moving Average (ARIMA) echnique [2] has been wiely use for ime series forecasing. Because of is populariy, he ARIMA moel has been use as a benchmar o evaluae many new moelling approaches [9]. However, ARIMA is a general univariae moel an i is evelope base on he assumpion ha he ime series being forecase are linear an saionary [3]. As we inicae earlier, ARIMA woul no be he righ echnique for preicion of exchange raes. The Arificial Neural Newors, he well-nown funcion approximaors in preicion an sysem moelling, has recenly shown is grea applicabiliy in ime-series analysis an forecasing [25-28]. ANN assiss mulivariae analysis. Mulivariae moels can rely on graer informaion, where no only he lagge ime series being forecas, bu also oher inicaors (such as echnical, funamenal, iner-marer ec. for financial mare), are combine o ac as preicors. In aiion, ANN is more effecive in escribing he ynamics of nonsaionary ime series ue o is unique non-parameric, non-assumable, noise-oleran an aapive properies. ANNs are universal funcion approximaors ha can map any nonlinear funcion wihou a priori assumpions abou he aa [3]. In several applicaions, Tang an Fishwich [22], Jhee an Lee [0], Kamruzzaman an Sarer [2-3], Wang an Leu [23], Hill e al. [8], an many oher researchers have shown ha ANNs perform beer han ARIMA moels, specifically, for more irregular series an for muliple-perio-ahea forecasing. Kaasra an Boy [] provie a general inroucion of how a neural newor moel shoul be evelope o moel financial an economic ime series. Many useful, pracical consieraions were presene in heir aricle. Zhang an Hu [28] analyse bacpropagaion neural newors' abiliy o forecas an exchange rae. Wang [24] cauione agains he angers of one-sho analysis since he inheren naure of aa coul vary. Klein an Rossin [4] prove ha he qualiy of he aa also affecs he preicive accuracy of a moel. More recenly, Yao e al. [25] evaluae he capabiliy of a bacpropagaion neural-newor moel as an opion price forecasing ool. They also recognise he fac ha neural-newor moels are conex sensiive an when suies of his ype are conuce, i shoul be as comprehensive as possible for ifferen mares an ifferen neural-newor moels. In his paper, we apply ANNs for preicing currency exchange raes of Ausralian Dollar agains six oher currencies such as US Dollar (USD), Grea Briish Poun (GBP), Japanese Yen (JPY), Singapore Dollar (SGD), New Zealan Dollar (NZD) an Swiss Franc (CHF) using heir hisorical exchange raes. Three ifferen ANNs base moels using he exising learning algorihms such as sanar bacpropagaion, scale conjugae graien an Baysian regularizaion were consiere. A oal of 500 hisorical exchange raes aa (closing rae of each wee), for each of six currency raes, were collece an use as inpus o buil he preicion moels in our suy, an hen aiional 65 exchange raes aa were use o evaluae he moels. The preicion resuls of all hese moels, for 35 an 65 wees, were compare base on five ifferen evaluaion inicaors such as Normalize Mean Square Error (NMSE), Mean Absolue Error (MAE), Direcional Symmery (DS), Correc Up ren (CU) an Correc Down ren (CD). The resuls show ha scale conjugae graien an Baysian regularizaion base moels show compeiive resuls an hese moels forecass more accuraely han sanar Bacpropagaion which has been suie consierably in oher suies. In secion 2, ANN forecasing moel an performance merics are efine. Secion 3 an secion 4 escribe experimenal resuls an conclusion, respecively. 2. Neural Newor Forecasing Moel Neural newors are a class of nonlinear moel ha can approximae any nonlinear funcion o an arbirary egree of accuracy an have he poenial o be use as forecasing ools in many ifferen areas. The mos commonly use neural newor archiecure is mulilayer feeforwar newor. I consiss of an inpu layer, an 50

3 Neural Informaion Processing - Leers an Reviews Vol. 3, No. 2, May 2004 oupu layer an one or more inermeiae layer calle hien layer. All he noes a each layer are connece o each noe a he upper layer by inerconnecion srengh calle weighs. A raining algorihm is use o aain a se of weighs ha minimizes he ifference he arge an acual oupu prouce by he newor. There are many ifferen neural ne learning algorihms foun in he lieraure. No suy has been repore o analyically eermine he generalizaion performance of each algorihm. In his suy, we experimene wih hree ifferen neural newor learning algorihms, namely sanar Bacpropagaion (BP), Scale Conjugae Graien Algorihm (SCG) an Bacpropagaion wih Regularizaion (BPR) in orer o evaluae which algorihm preics he exchange rae of Ausralian ollar mos accuraely. In he following we escribe he algorihms briefly. 2. Learning Algorihms Sanar Bacpropagaion (SBP): Bacpropagaion [2] upaes he weighs ieraively o map a se of inpu vecors (x,x 2,,x p ) o a se of corresponing oupu vecors (y,y 2,,y p ). The inpu x p is presene o he newor an muliplie by he weighs. All he weighe inpus o each uni of upper layer are summe up, an prouce oupu governe by he following equaions. y = f ( W h + θo ), () p h ( ), p = f Wh xp + θh (2) where W o an W h are he oupu an hien layer weigh marices, h p is he vecor enoing he response of hien layer for paern p, θ o an θ h are he oupu an hien layer bias vecors, respecively an f(.) is he sigmoi acivaion funcion. The cos funcion o be minimize in sanar Bacpropagaion is he sum of square error efine as T E = ( p y p ) ( p y ) (3) p 2 p where p is he arge oupu vecor for paern p. The algorihm uses graien escen echnique o ajus he connecion weighs beween neurons. Denoing he fan-in weighs o a single neuron by a weigh vecor w, is upae in he -h epoch is governe by he following equaions. w η E ( ) () w w w + α w - o p = = (4) The parameers η an α are he learning rae an he momenum facor, respecively. The learning rae parameer conrols he sep size in each ieraion. For a large-scale problem Bacpropagion learns very slowly an is convergence largely epens on choosing suiable values of η an α by he user. Scale Conjugae Graien (SCG): The error surface in Bacpropagaion may conain long ravines wih sharp curvaure an genly sloping floor which causes slow convergence. In conjugae graien mehos, a search is performe along conjugae irecions, which prouces generally faser convergence han seepes escen irecions [7]. In seepes escen search, a new irecion is perpenicular o he ol irecion. This approach o he minimum is a zigzag pah an one sep can be mosly unone by he nex. In conjugae graien mehos, a new search irecion spoils as lile as possible he minimizaion achieve by he previous irecion an he sep size is ajuse in each ieraion. The general proceure o eermine he new search irecion is o combine he new seepes escen irecion wih he previous search irecion so ha he curren an previous search irecions are conjugae. Conjugae graien echniques are base on he assumpion ha, for a general nonquaraic error funcion, error in he neighborhoo of a given poin is locally quaraic. The weigh changes in successive seps are given by he following equaions. wih w w g α + = + (5) = + β (6) g E ( w) w = w T T T g g g g g g β = or β = or β = (8) T T T g g g g g where an - are he conjugae irecions in successive ieraions. The sep size is governe by he coefficien α an he search irecion is eermine by β. In scale conjugae graien he sep size α is calculae by he following equaions. (7) 5

4 ANN-Base Forecasing of Foreign Currency Exchange Rae J. Kamruzzaman an R. Sarer α T g = (9) δ T δ + 2 = H λ (0) where λ is he scaling co-efficien an H is he Hessian marix a ieraion. λ is inrouce because, in case of non-quaraic error funcion, he Hessian marix nee no be posiive efinie. In his case, wihou λ, δ may become negaive an weigh upae may lea o an increase of error funcion. Wih sufficienly large λ, he moifie Hessian is guaranee o be posiive (δ > 0). However, for large values of λ, sep size will be small. If he error funcion is no quaraic or δ <0, λ can be increase o mae δ >0. In case of δ <0, Moller [9] suggese he appropriae scale coefficien λ o be Rescale value δ of δ is hen be expresse as δ = δ + ( ) δ λ = 2 λ () 2 λ The scale coefficien also nees ajusmen o valiae he local quaraic approximaion. The measure of quaraic approximaion accuracy, is expresse by λ 2 E( w + α )} T g (2) 2{ E( w ) = (3) α If is close o hen he approximaion is a goo one an he value of λ can be ecrease []. On he conrary if is small, he value of λ has o be increase. Some prescribe values suggese in [9] are as follows For > 0.75, λ + =λ /2; For < 0.25, λ + =4λ ; Oherwise, λ + =λ Bayesian Reguralizaion (BPR): A esire neural newor moel shoul prouce small error no only on sample aa bu also on ou of sample aa. To prouce a newor wih beer generalizaion abiliy, MacKay [7] propose a meho o consrain he size of newor parameers by regularizaion. Regularizaion echnique forces he newor o sele o a se of weighs an biases having smaller values. This causes he newor response o be smooher an less liely o overfi [7] an capure noise. In regularizaion echnique, he cos funcion F is efine as F = γ E D + ( γ ) EW (4) 2 where E D is he same as E efine in Eq. (3), E w = w / 2 is he sum of squares of he newor parameers, an γ (<.0) is he performance raio parameer, he magniue of which icaes he emphasis of he raining on regularizaion. A large γ will rive he error E D o small value whereas a small γ will emphasize parameer size reucion a he expense of error an yiel smooher newor response. One approach of eermining opimum regularizaion parameer auomaically is he Bayesian framewor [7]. I consiers a probabiliy isribuion over he weigh space, represening he relaive egrees of belief in ifferen values for he weighs. The weigh space is iniially assigne some prior isribuion. Le D={x m, m } be he aa se of he inpu-arge pair, m being a label running over he pair an M be a paricular NN moel. Afer he aa is aen, he poserior probabiliy isribuion for he weigh p(w D,γ,M) is given accoring o he Bayesian rule. p(d w, γ, M ) p( w γ, M) p( w D, γ, M ) = (5) p(d γ, M) where p(w γ,m) is he prior isribuion, p(d w,γ,m) is he lielihoo funcion an p(d γ,m) is a normalizaion facor. In Bayesian framewor, he opimal weigh shoul maximize he poserior probabiliy p(w D,γ,M), which is equivalen o maximizing he funcion in Eq.(4). The performance raion parameer is opimize by applying he Bayes rule p(d γ, M ) p( γ M) p( γ D, M ) = (6) p(d M) 52

5 Neural Informaion Processing - Leers an Reviews Vol. 3, No. 2, May 2004 If we assume a uniform prior isribuion p(γ M) for he regularizaion parameer γ, hen maximizing he poserior probabiliy is achieve by maximizing he lielihoo funcion p(d γ,m). Since all probabiliies have a Gaussian form i can be expresse as N / 2 L / 2 p( D γ, M ) = ( π / γ ) [ π /( γ )] Z F ( γ ) (7) where L is he oal number of parameers in he NN. Supposing ha F has a single minimum as a funcion of w a w* an has he shape of a quaraic funcion in a small area surrouning ha poin, Z F is approximae as [7] L / 2 2 * * Z / F ( 2π ) e H exp( F( w )) (8) where H=γ 2 E D +(-γ) 2 E W is he Hessian marix of he objecive funcion. Using Eq. (8) ino Eq. (7), he opimum value of γ a he minimum poin can be eermine. Foresee an Hagan [6] propose o apply Gauss-Newon approximaion o Hessian marix, which can be convenienly implemene if he Lebenberg-Marquar opimizaion algorihm [20] is use o locae he minimum poin. This minimizes he aiional compuaion require for regularizaion. 2.2 Forecasing Moel Technical an funamenal analyses are he wo major financial forecasing mehoologies. In recen imes, echnical analysis has rawn paricular acaemic ineres ue o he increasing evience ha mares are less efficien han was originally hough [5]. Lie many oher economic ime series moel, exchange rae exhibis is own ren, cycle, season an irregulariy. In his suy, we use ime elay moving average as echnical aa. The avanage of moving average is is enency o smooh ou some of he irregulariy ha exis beween mare ays [26]. In our moel, we use moving average values of pas wees o fee o he neural newor o preic he following wee s rae. The inicaors are MA5, MA0, MA20, MA60, MA20 an X i, namely, moving average of one wee, wo wees, one monh, one quarer, half year an las wee's closing rae, respecively. The preice value is X i+. So he neural newor moel has 6 inpus for six inicaors, one hien layer an one oupu uni o preic exchange rae. Yao e al. [26] has repore ha increasing he number of inpus oes no necessarily improve he performance. Hisorical aa are use o rain he moel. Once raine he moel is use for forecasing. 3. Experimenal Resuls an Discussion In he following, we escribe he forex aa collecion, performance merics o evaluae an compare he preicive power of he moels an he simulaion resuls. 3. Daa collecion The aa use in his suy is he foreign exchange rae of six ifferen currencies agains Ausralian ollar from January 99 o July 2002 mae available by he Reserve Ban of Ausralia. We consiere exchange rae of US ollar (USD), Briish Poun (GBP), Japanese Yen (JPY), Singapore ollar (SGD), New Zealan ollar (NZD) an Swiss Franc (CHF). As ouline in Secion 2.2, 565 weely aa was consiere of which firs 500 weely aa was use is raining an he remaining 65 weely aa for evaluaing he moel. The plos of hisorical raes for USD, GBP, SGD, NZD, CHF are shown in Fig. (a) an for JPY in Fig. (b). Exchange Rae.6 20 USD GBP SGD.4 NZD CHF 00 JPY Wee Number Wee Number (a) (b) Figure. Hisorical exchange raes for (a) USD, GBP, SGD, NZD an CHF (b) JPN agains Ausralian ollar. Exchange rae 53

6 ANN-Base Forecasing of Foreign Currency Exchange Rae J. Kamruzzaman an R. Sarer 3. 2 Performance Merics The forecasing performance of he above moel is evaluae agains a number of wiely use saisical meric, namely, Normalize Mean Square Error (NMSE), Mean Absolue Error (MAE), Direcional Symmery (DS), Correc Up ren (CU) an Correc Down ren (CD). These crieria are efine in Table. x an xˆ are he acual an preice values, respecively. NMSE an MAE measure he eviaion beween acual an forecas value. Smaller values of hese merics inicae higher accuracy in forecasing. Aiional evaluaion measures inclue he calculaion of correc maching number of he acual an preice values wih respec o sign an irecional change. DS measures correcness in preice irecions while CU an CD measure he correcness of preice up an own ren, respecively. Table : Performance Merics o Evaluae he Forecasing Accuracy of he Moel. ( x NMSE = = ( x ) 2 2 N ( x ) x ) MAE = x N 00 DS = N, CU = 00, 2 σ if ( x x ) ( x = 0 oherwise 2 ˆ ) 0 = if ( xˆ ) > 0, ( x x ) ( xˆ ) 0, 0 oherwise CD = 00 ˆ ) 0, if ( x ) < 0, ( x x ) ( xˆ = 0 oherwise x x if ( ) > 0 = 0 oherwise x x if ( ) < 0 = 0 oherwise 3.3 Simulaion Resuls A neural newor moel was raine wih six inpus represening he six echnical inicaors, a hien layer an an oupu uni o preic he exchange rae. The final se of weighs o which a newor seles own (an hence is performance) epens on a number of facors, e.g., iniial weighs chosen, ifferen learning parameers use uring raining (escribe in secion 2.) an he number of hien unis. For each algorihm, we raine 30 ifferen newors wih ifferen iniial weighs an learning parameers. The number of hien unis was varie beween 3~7 an he raining was erminae a ieraion number beween 5000 o The newor ha yiele he bes resul ou of he 30 rials in each algorihm is presene here. We measure he performance merics on he es aa o invesigae how well he neural newor forecasing moel capure he unerlying ren of he movemen of each currency agains Ausralian ollar. Table 2 shows he performance merics achieve by each moel over a forecasing perio of 35 wees an Table 3 shows he same over 65 wees (previous 35 wees plus aiional 30 wees). The resuls show ha SCG an BPR moel consisenly performs beer han SBP moel in erms of all performance merics in almos all he currency exchange raes. For example, in case of forecasing US ollar rae over 35 wees, NMSE achieve by SCG an BPR is quie low an is almos half of ha achieve by SBP. This means hese moels are capable of preicing exchange raes more closely han SBP. Also, in preicing ren irecions SCG an BPR is almos 0% more accurae han SBP. The reason of beer performance by SCG an BPR algorihm is he improve learning echnique which allows hem o search efficienly in weigh space for soluion. Similar ren is observe in preicing oher currencies. 54

7 Neural Informaion Processing - Leers an Reviews Vol. 3, No. 2, May 2004 Table 2: Measuremen of Preicion Performance over 35 Wee Preicion NN Performance merics Currency moel NMSE MAE DS CU CD SBP US. SCG Dollar BPR SBP B. Poun SCG BPR SBP J. Yen SCG BPR SBP S. Dollar SCG NZ Dollar S. Franc BPR SBP SCG BPR SBP SCG BPR Table 3: Measuremen of Preicion Performance over 65 Wee Preicion. Performance merics Currency NN moel NMSE MAE DS CU CD SBP US. SCG Dollar BPR SBP B. Poun SCG BPR SBP J. Yen SCG BPR SBP S. Dollar SCG NZ Dollar S. Franc BPR SBP SCG BPR SBP SCG BPR Beween SCG an BPR moels, he former performs beer in all currencies excep Japanese Yen in erms of he wo mos commonly use crieria, i.e., NMSE an MAE. In erms of oher merics, SCG yiels slighly beer performance in case of Swiss France, BR slighly beer in US Dollar an Briish Poun, boh perform equally in case of Japanese Yen, Singapore an New Zealan Dollar. In boh algorihms, he irecional change preicion accuracy is above 80% which is much improvemen han he 70% accuracy achieve in [26] in a similar suy. The comparaive iagrams showing he oupu forecas by neural newor moel an acual ime series over 65 wees for six currencies are shown in Fig. 2(a)~(f). Fig 2(a) show he forecasing of USD by all he hree moels. The plos show ha he forecasing by SCG an BPR moels more closely follows he acual rae. For oher currencies SCG moel preicion is very close o he acual exchange rae. In his suy, we also invesigae he influence of neural newor archiecure on preicion performance. Using SCG learning algorihm, he moel was raine wih ifferen number of hien unis o preic USD agains AUD. Ou of 30 successful rials, he preicion performance of he bes rial is repore in Table 4. The archiecure of he newor is enoe by i-h-o inicaing i neurons in inpu layer, h neuron in hien layer an o neuron in oupu layer. The performance varies wih he number of hien unis. However, in all cases he performance is beer han ha of SBP moel. The bes performance is achieve wih hree unis, increasing he number of hien noes (afer hree) eerioraes he performance. Table 4: Effec of hien uni number on preicion performance. Archiec 35 wee preicion 65 wee preicion ure NMSE MAE DS CU CD NMSE MAE DS CU CD The generalizaion abiliy of neural newors, i.e., is abiliy o prouce correc oupu in response o an unseen inpu is influence by a number of facors: ) he size of he raining se, 2) he egrees of freeom of he newor relae o he archiecure, an 3) he physical complexiy of he problem a han. Pracically we have 55

8 ANN-Base Forecasing of Foreign Currency Exchange Rae J. Kamruzzaman an R. Sarer Acual Forecas (SBP) Forecas (BPR) Forecas (SCG) Acual Forecas (SCG) (a) USD/AUD (b) GBP/AUD Acual Forecas (SCG).05 Acual Forecas (SCG) (c) JPY/AUD 0.85 () SGD/AUD Acual Forecas (SCG) 0.95 Acual Forecas (SCG) (e) NZD/AUD 0.75 (f) CHF/AUD Figure 2. Forecasing of ifferen currencies by SCG base neural newor moel over 65 wees. no conrol on he problem complexiy, an in our simulaion he size of he raining se is fixe. This leaves he generalizaion abiliy, i.e., performance of he moel epenen on he archiecure of he corresponing neural newor. Generalizaion performance can also be relae o he complexiy of he moel in he sense ha, in orer o achieve bes generalizaion, i is imporan o opimize he complexiy of he preicion moel []. In case of neural newors, he complexiy can be varie by changing he number of aapive parameers in he newor. A newor wih fewer weighs is less complex han one wih more weighs. I is nown ha he simples hypohesis/moel is leas liely o overfi. A newor ha uses he leas number of weighs an biases o achieve a given mapping is leas liely o overfi he aa an is mos liely o generalize well on he unseen aa. If reunancy is ae in he form of exra hien uni or aiional parameers, i is liely o egrae 56

9 Neural Informaion Processing - Leers an Reviews Vol. 3, No. 2, May 2004 performance because more han he necessary number of parameers is use o achieve he same mapping. In case nonlinear regression, wo exreme soluions shoul be avoie: filering ou he unerlying funcion or unerfiing (no enough hien neurons), or moeling of noise or overfiing aa (oo many hien neurons). This siuaion is also nown as bias-variance ilemma. One way of conrolling he effecive complexiy of he moel in pracice is o compare a range of moels having ifferen archiecures an selec he one ha yiels bes performance on he es aa. As can be seen in our simulaion ha he newor wih 3 hien unis is opimum yieling bes performance. Increasing he hien unis as aiional parameers, inrouces reunancy an eerioraes he performance. 4. Conclusion an furher Research This paper has presene an compare hree ifferen neural newor moels o perform foreign currency exchange forecasing using simple echnical inicaors. Scale conjugae graien base moel achieves closer preicion of all he six currencies han oher moels. As Meeiros e al. argues in [8], here are eviences ha favour linear an nonlinear moels agains ranom wal, an nonlinear moels san a beer chance when nonlineariy is sprea in ime series. A neural newor moel wih improve learning echnique is hus a promising caniae for forex preicion. Resuls in his suy shows ha SCG neural newor moel achieves very close preicion in erms of NMSE an MAE merics. Several auhors has argue ha irecional change merics may be a beer sanar for eermining he qualiy of forecasing. In erms of his meric, SCG moel achieves comparable resuls o BPR moel. However, which meric shoul be given more imporance epens on raing sraegies an how he preicion is use for raing avanages [25]. Boh SCG an BPR base moels aain significanly high rae of preicing correc irecional change (above 80%). In his suy, we consiere six echnical inicaors as inpus. Some oher echnical inicaors lie RSI (relaive srengh inex), momenums can also be consiere. In ha case sensiiviy analysis may be one o eliminae less sensiive variables. We invesigae he effec of newor archiecure on performance merics. The performance varies slighly wih he number of unis in hien layer. The opimum number of hien unis nees o be eermine by rial an error. In [26] Yao e al. ouline he nee for an auomaic moel builing faciliy o avoi eious rial an error meho. This can be achieve by employing a consrucive algorihm [6] ha sars wih a minimum archiecure an auomaically grows by incremenally aing hien unis an layers one by one. I is claime ha his ype of archiecure is mos liely o buil an opimum or near opimum archiecure auomaically. This woul furher a he flexibiliy of he moel bu is performance in forex preicion nees o be invesigae. Chan e al. [4] has applie PNN (Probabilisic Neural Newor) for forecasing an raing of soc inex wih a view ha raining PNN is faser ha enables he user o evelop a frequenly upae raining scheme. In acual applicaions, reraining of a forecasing moel wih he mos recen aa may be necessary o increase he chance of achieving a beer forecas. Fas learning may be an avanage bu i oes no always guaranee an improve performance. A comparison beween PNN-base forecasing moel an our moel, wih reraining a some inerval, will assess he suiabiliy of he moel in such applicaion. Furher invesigaion in his irecion will focus on formulaing an objecive funcion in ANN moel ha aes oher gooness measures e.g., raing sraegies an profi ino consieraion. Recenly several applicaions of combining wavele ransformaion in financial ime series forecasing has been propose. A hybri sysem using wavele echniques in neural newors loos promising [29]. However, fining he bes way of combining wavele echniques an neural newors in forex preicion nees o be invesigae an remains he focus of fuure research. References [] C.M. Bishop, Neural Newors for Paern Recogniion, Oxfor Universiy Press, NY, 995. [2] G. E. P. Box an G. M. Jenins, Time Series Analysis: Forecasing an Conrol, Holen-Day, San Francosco, CA, 990. [3] L. Cao an F. Tay, Financial forecasing using suppor vecor machines, Neural Compu. & Applic, vol. 0, pp.84-92, 200. [4] A. Chen, M. Leung an H. Daou, Applicaion of neural newros o an emerging financial mare: forecasing an raing he Taiwan Soc Inex, Compuer & Operaions Research, vol. 30, pp , [5] G. Deboec, Traing on he Ege: Neural, Geneic an Fuzzy Sysems for Chaoic Financial Mares, New Yor Wiley, 994. [6] F. D. Foresee an M.T. Hagan, Gauss-Newon approximaion o Bayesian regularizaion, Proc. IJCNN 997, pp , 997. [7] M.T. Hagan, H.B. Demuh an M.H. Beale, Neural Newor Design, PWS Publishing, Boson, MA,

10 ANN-Base Forecasing of Foreign Currency Exchange Rae J. Kamruzzaman an R. Sarer [8] T. Hill, M. O Connor an W. Remus, Neural newor moels for ime series forecass, Managemen Science, vol. 42, pp , 996. [9] H. B. Hwarng an H. T. Ang, A simple neural newor for ARMA(p,q) ime series, OMEGA: In. Journal of Managemen Science, vol. 29, pp , [0] W. C. Jhee an J. K. Lee, Performance of neural newors in managerial forecasing, Inelligen Sysems in Accouning, Finance an Managemen, vol. 2, pp 55-7, 993. [] I. Kaasra an M. Boy, Designing a neural newor for forecasing financial an economic ime-series, Neurocompuing, vol. 0, pp , 996. [2] J. Kamruzzaman an R. Sarer, Comparing ANN base moels wih ARIMA for preicion of forex raes, ASOR Bullein, vol. 22, pp. 2-, [3] J. Kamruzzaman an R. Sarer, Forecasing of currency exchange raes using ANN: a case suy, Proc. of IEEE In. Conf. on Neural Newors & Signal Processing (ICNNSP03), pp , [4] B. D. Klein an D. F. Rossin, Daa qualiy in neural newor moels: effec of error rae an magniue of error on preicive accuracy, OMEGA: In. Journal of Managemen Science, vol. 27, pp , 999. [5] B. LeBaron, Technical raing rule profiabiliy an foreign exchange inervenion, Journal of In. Economics, vol. 49, pp , 999. [6] M. Lehoangas, Moifie consrucive bacpropagaion for regression, Neurocompuing, vol. 35, pp. 3-22, [7] D.J.C. Macay, Bayesian inerpolaion, Neural Compuaion, vol. 4, pp , 992. [8] M.C. Meeiros, A. Veiga an C.E. Pereira, Moeling exchange raes: smooh ransiions, neural newor an linear moels, IEEE Trans. Neural Newors, vol. 2, no. 4, 200. [9] A.F. Moller, A scale conjugae graien algorihm for fas supervise learning, Neural Newors, vol. 6, pp , 993. [20] J.J. More, The Levenberg-Marquar algorihm: implemenaion an heory, in: G.A. Wason, e., Numerical analysis, Lecure Noes in Mahemaics 630, pp. 05-6, Springer-Verlag, Lonon, 977. [2] D.E Rumelhar, J.L. McClellan an he PDP research group, Parallel Disribue Processing, vol., MIT Press, 986. [22] Z. Tang an P. A. Fishwich, Bacpropagaion neural nes as moels for ime series forecasing, ORSA Journal on Compuing, vol. 5, no. 4, pp , 993. [23] J. H.Wang an J. Y. Leu, Soc mare ren preicion using ARIMA-base neural newors, Proc. of IEEE In. Conf. on Neural Newors, vol. 4, pp , 996. [24] S. Wang, An insigh ino he sanar bac-propagaion neural newor moel for regression analysis, OMEGA: In. Journal of Managemen Science, vol. 26, pp.33-40, 998. [25] J. Yao, Y. Li an C. L. Tan, Opion price forecasing using neural newors, OMEGA: In. Journal of Managemen Science, vol. 28, pp , [26] J. Yao an C.L. Tan, A case suy on using neural newors o perform echnical forecasing of forex, Neurocompuing, vol. 34, pp , [27] S. Yaser an A. Aiya, Inroucion o Financial Forecasing, Applie Inelligence, vol. 6, pp , 996. [28] G. Zhang an M. Y. Hu, Neural newor forecasing of he Briish Poun/US ollar exchange rae, OMEGA: In. Journal of Managemen Science, vol. 26, pp , 998. [29] B. Zhang, R. Coggins, M. Jabri, D. Dersch an B. Flower, Muliresoluion forecasing for fuure raing using wavele ecomposiion, IEEE Trans. Neural Newors, special issue in Financial Engg., vol. 2, no.4, pp , Joarer Kamruzzaman receive his B.Sc an M.Sc in Elecrical Engineering from Banglaesh Universiy of Engineering an Technology, Dhaa, Banglaesh in 986 an 989 respecively, an PhD in Informaion Sysems Engineering from Muroran Insiue of Technology, Japan in 993. Currenly he is a faculy member in he Faculy of Informaion Technology, Monash Universiy, Ausralia. His research ineres inclues neural newors, fuzzy sysem, geneic algorihm, compuer newors an bioinformaics ec. Ruhul Sarer receive his Ph.D. in 99 from DalTech, Dalhousie Universiy, Halifax, Canaa, an is currenly a senior faculy member in he School of Informaion Technology an Elecrical Engineering, Universiy of New Souh Wales, ADFA Campus, Canberra, Ausralia. His main research ineress are Evoluionary Opimizaion, Neural Newors an Applie Operaions Research. He has recenly eie four boos an has publishe more han 90 referee papers in inernaional journals an conference proceeings. Dr Sarer is acively involve wih a number of naional an inernaional conferences & worshop organizaions in he capaciy of chair / co-chair or program commiee member. He has recenly serve as a echnical co-chair for IEEE-CEC2003. He is also a member of as force for promoing evoluionary muli-objecive opimizaion operae by IEEE Neural Newor Sociey. 58