On forecasting exchange rates using neural networks

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<ul><li><p>This article was downloaded by: [Moskow State Univ Bibliote]On: 18 February 2014, At: 01:28Publisher: RoutledgeInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: MortimerHouse, 37-41 Mortimer Street, London W1T 3JH, UK</p><p>Applied Financial EconomicsPublication details, including instructions for authors and subscriptioninformation:http://www.tandfonline.com/loi/rafe20</p><p>On forecasting exchange rates using neuralnetworksPhilip Hans Franses &amp; Paul van HomelenPublished online: 07 Oct 2010.</p><p>To cite this article: Philip Hans Franses &amp; Paul van Homelen (1998) On forecasting exchange rates using neuralnetworks, Applied Financial Economics, 8:6, 589-596, DOI: 10.1080/096031098332628</p><p>To link to this article: http://dx.doi.org/10.1080/096031098332628</p><p>PLEASE SCROLL DOWN FOR ARTICLE</p><p>Taylor &amp; Francis makes every effort to ensure the accuracy of all the information (the Content)contained in the publications on our platform. However, Taylor &amp; Francis, our agents, and our licensorsmake no representations or warranties whatsoever as to the accuracy, completeness, or suitabilityfor any purpose of the Content. Any opinions and views expressed in this publication are the opinionsand views of the authors, and are not the views of or endorsed by Taylor &amp; Francis. The accuracy ofthe Content should not be relied upon and should be independently verified with primary sourcesof information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings,demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arisingdirectly or indirectly in connection with, in relation to or arising out of the use of the Content.</p><p>This article may be used for research, teaching, and private study purposes. Any substantial orsystematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distributionin any form to anyone is expressly forbidden. Terms &amp; Conditions of access and use can be found athttp://www.tandfonline.com/page/terms-and-conditions</p></li><li><p>Applied Financial Economics, 1998, 8, 589 596</p><p>On forecasting exchange rates using neuralnetworks</p><p>PHILIP HANS FRANSES and PAUL VAN HOMELEN*</p><p>Econometric Institute and Rotterdam Institute for Business Economic Studies, ErasmusUniversity Rotterdam, The Netherlands and *Institute for Research and InvestmentServices, Rotterdam, The Netherlands</p><p>The paper considers the modelling, description and forecasting of four daily exchangerate returns relative to the Dutch guilder using arti cial neural network models(ANNs). Based on simulations it is argued (i) that neglected GARCH does not lead tospuriously successful ANNs and (ii) that if there is some form of nonlinearity otherthan GARCH, ANNs will exploit this for improved forecasting. For the sample data itis found that ANNs do not yield favourable in-sample ts or forecasting performance.These results are interpreted as indicating that the nonlinearity often found inexchange rates is most likely due to GARCH and therefore ANNs are recommendedas a diagnostic for mean nonlinearity.</p><p>I . INTRODUCTION</p><p>When daily or weekly nancial time series are analysedusing tests for generalized autoregressive conditional hete-roscedasticity (GARCH) or for other forms of nonlinearity,one typically nds empirical evidence for both features.Bollerslev et al. (1992) summarize many studies involvingGARCH, while for example Hsieh (1988 and 1989) andScheinkman and LeBaron (1989) nd substantial nonlin-earity in nancial data. The key di erence between GARCHmodels and many other nonlinear models is that theGARCH model usually cannot be exploited to generatenonzero out-of-sample forecasts for the returns of a nan-cial asset, while many nonlinear models can be used as such.In fact, the GARCH model is speci cally designed to gener-ate out-of-sample forecasts for the variance of a series ofreturns, and hence this model is often used for optionpricing, among other uses.Recent applications of arti cial neural network models</p><p>(ANNs) to exchange rates in, for example, Kuan and Liu(1995), Swanson and White (1995) and Genay (1996) showthat these models can describe in-sample data rather well,and that they also sometimes generate good out-of-sampleforecasts, where g`ood is usually de ned in terms of smallmean squared prediction error or in terms of directionalaccuracy of the forecasts. An ANN can be viewed as a gen-eral nonlinear time series model, and hence the apparent</p><p>nonlinear features in the daily exchange rate data analysedin the above studies seem to be picked up by the ANNs.Recent results documented in Brooks (1996), however, sug-gest that such nonlinear features, which are often elicited bystatistical tests and by the success of empirical nonlinearmodels tted to the data, may be due to neglected GARCH.In other words, it may be that GARCH in daily exchangerates leads to the nding of forms of nonlinearity which inturn may suggest that one can forecast the returns on theexchange rates themselves. Obviously, when GARCH leadsto the spurious application of nonlinear models such asneural networks, there may be no forecasting gain.In this paper we aim to contribute to the area of research</p><p>using ANNs to describe and forecast daily exchange ratereturns by analysing the possible e ects of GARCH. Simu-lation experiments are used to investigate the possibilitythat ANNs mistakenly pick up GARCH properties of thedata, and hence mistakenly suggest that the returns series canbe forecasted. In the same set of simulation experiments wealso examine whether some speci c forms of nonlinearity,where two bilinear models and one exponential autoregres-sive (EAR) model are included, can be captured by the moregeneral (and possibly overparameterized) ANN. To mimica realistic practical situation we focus on the fraction oftimes that a model adequately forecasts the sign of thereturn on the following day. For four daily exchange rates,the US and Canadian dollars, the British pound and the</p><p>0960 3107 1998 Routledge 589</p><p>Dow</p><p>nloa</p><p>ded </p><p>by [M</p><p>osko</p><p>w St</p><p>ate U</p><p>niv B</p><p>ibliot</p><p>e] at </p><p>01:28</p><p> 18 Fe</p><p>brua</p><p>ry 20</p><p>14 </p></li><li><p>Japanese Yen (all versus the Dutch guilder), the in sample t and out-of-sample predictive performance of variousANNs is evaluated. Several possible model variants con-cerning lag structures and the number of hidden layer cellsare considered since this allows one to evaluate whetheroften applied model selection criteria result in good fore-casting models.The outline of the paper is as follows. In the next section,</p><p>the empirical strategy which is followed throughout thispaper is described. In Section III, the results of some simula-tion exercises are presented. In Section IV, the outcomes ofmodelling and forecasting four daily exchange rate series arepresented. In Section V it is concluded that these ndingsadd to recent work by Brooks (1996), in the sense thatapparent nonlinearity in exchange rates seems due toGARCH, and some suggestions for further research areprovided.</p><p>II . EMPIRICAL APPROACH</p><p>Consider a daily observed real exchange rate series xt, witht = 0, 1, 2, , n and de ne the returns yt as yt = log(xt/xt 1 ) for t = 1, 2, , n, where log denotes the natural log-arithm. In this paper, we aim to describe yt by the arti cialneural network model with a linear component, i.e.</p><p>yt = m + / 1yt 1 + / 2yt 2 + + / pyt p</p><p>+q</p><p>+j = 1b jG (m j + / 1 jyt 1 + / 2 jyt 2 + + / pjyt p)</p><p>+ e t (1)</p><p>with</p><p>G (a) = (1 + exp( - a)) 1 (2)</p><p>where e t is some error process, and where m , / 1 to / p, b j , m jand / 1 j to / pj are unknown parameters, for j = 1, 2, , q.Hence, the model contains (q + 1) (p + 2) - 1 parameters.The ANN model in Equations 1 2 contains p lags of yt andq so-called hidden layer cells. G (a) is the logistic activationfunction, which connects the p + 1 input components (i.e.p lagged yt variables and a constant) with the hidden layer.The hidden layer is connected with the output variableyt through the b j parameters. The model in Equation 1 canbe abbreviated as an ANN(p, q, 1) model. Model 1 2 is oftenused in the empirical analysis of economic and nancialtime series data (Swanson and White, 1995; Kuan and Liu,1995). One possible motivation for its frequent use is thatKuan and White (1994), for example show that with largeenough q, an ANN can approximate (with arbitrary pre-cision) any function f that connects yt with its past realiz-ations, i.e. any function f in yt = f (yt 1 , , yt p) + e t .This property of ANNs make them useful in recognizinga variety of patterns in time series data with great precision;</p><p>see, for example, Ripley (1994), Bishop (1995) and Fransesand Draisma (1997). This also leads to our choice of anANN to describe and forecast potentially nonlinear dailyexchange rate data.The parameters in the ANN are estimated by minimizing</p><p>the residual sum of squares. In the rst round of optimiza-tion, a penalty is imposed on the values of the parameters, asis advocated in Ripley (1994). In the last round, this penaltyis removed. The estimation procedure uses the simplexmethod of Nelder and Mead and the Broyden Fletcher Goldfarb Shanno algorithm, of which the latter is avail-able in the Gauss optimization toolbox (version 3.1.1).The Gauss programs are available from the authors onrequest.The parameters in Equation 1 are estimated for p, q </p><p>{1, 2, 3, 4, 5}. Hence, we do not explicitly focus on the linearmodel (i.e. the case where q = 0) but allow for at least somedegree of nonlinearity in our simulated data and our sampleseries. This leads to the estimation of parameters in 25di erent ANN models. All these models will be used forout-of-sample forecasting. In doing so, we will be able toexamine whether certain in-sample model selection criteria,such as the Akaike and Schwarz information criteria, lead togood forecasting models.We focus on describing a time series of returns yt by the</p><p>ANNmodel in Equations 1 and 2 for the rst n observationsand on forecasting the next m observations n + 1 to n + m.Then the estimation sample is shifted to m + 1 until n + m,and the observations in n + m + 1 to n + 2m are forecast. Intotal there are n + 4m observations, and hence four modelevaluation samples. Notice that the in-sample model selec-tion criteria to be calculated below are averages over thesefour cases. One-step ahead forecasting only is considered,i.e. the model structure and the values of the tted para-meters (obtained from the rst n data points) are heldconstant, while the truly observed data yn+ k to forecastyn+ k+ 1 , for k = 1, 2, , m - 1 are used. In simulation ex-periments, n was set at 750 and m at 250, since for dailyobserved returns this roughly corresponds to three years ofdata to t the model, and one year of data to evaluate theforecasts, respectively. For larger values of n and othervalues of m the results obtained were not qualitativelydi erent from those reported in the next two sections.There are several approaches to evaluate the in-sample</p><p>and out-of-sample performance of time series models.For the in-sample performance the Akaike and Schwarzinformation criteria is used to indicate the best model.Additionally, and in order to mimic a practically realisticsituation, it is investigated whether or not the sign of the tted return yW t equals that of the truly observed return yt , fort = 1, 2, , n. For this purpose, the success ratio (SR) isde ned as</p><p>SR = n 1n</p><p>+t= 1</p><p>It[yt yW t &gt; 0]</p><p>590 P. H. Franses and P. Van Homelen</p><p>Dow</p><p>nloa</p><p>ded </p><p>by [M</p><p>osko</p><p>w St</p><p>ate U</p><p>niv B</p><p>ibliot</p><p>e] at </p><p>01:28</p><p> 18 Fe</p><p>brua</p><p>ry 20</p><p>14 </p></li><li><p>where It[ . ] is an indicator function that takes a value of1 when its argument is true and a value of 0 otherwise.The out-of-sample forecasts are also evaluated by com-</p><p>paring the sign of the forecast observation yW n+ i with the truewithheld observation yn+ i , for i = 1, 2, , m. Again, weuse the SR measure, which for the out-of-sample data isgiven by</p><p>SR = m 1m</p><p>+i= 1</p><p>Ii[yn+ i yW n+ i &gt; 0] (3)</p><p>For the out-of-sample forecasts, it is tested whether or notthe SR value in Equation 3 di ers signi cantly from an SRvalue that would be obtained in the case where the yn+ i andyW n+ i are independent. For this purpose, the test proposed inPesaran and Timmermann (1992) is used. De ne</p><p>P = m 1m</p><p>+i= 1</p><p>Ii[yn+ i &gt; 0]</p><p>and</p><p>P = m 1m</p><p>+i= 1</p><p>Ii[yW n+ i &gt; 0]</p><p>then the success rate in the case of independence (SRI) ofyn+ i and yW n+ i is given by</p><p>SRI = PP + (1 - P) (1 - P )</p><p>with variance</p><p>var(SR) = m 1 SRI(1 - SRI). (4)</p><p>The variance of SR in Equation 3 is given by</p><p>var(SRI) = m 2 [m (2P - 1)2 P(1 - P) + m (2P - 1)2 P (1 - P )</p><p>+ 4PP (1 - P) (1 - P )]. (5)</p><p>The directional accuracy (DA) test of Pesaran and Timmer-mann (1992) is now calculated as</p><p>DA = [var(SR) - var (SRI)] 1 /2 (SR - SRI) (6)</p><p>Pesaran and Timmermann (1992) show that under the nullhypothesis that yn+ i and yW n+ i are independently distributed,the DA test follows the standard normal distribution. In thispaper, the null hypothesis is evaluated in a two-sided testprocedure since we also want to allow for signi cantly poorforecasts.</p><p>II I . SOME SIMULATION RESULTS</p><p>Before analysing the set of daily exchange rate series, theproposed empirical approach is evaluated using some simu-lation experiments. The rst set of experiments is motivatedby the nding that many daily exchange rate series displayGARCH properties (Baillie and Bollerslev, 1989), and by the nding that tests for neural network nonlinearity havepower against GARCH (Tera svirta et al., 1993; Brooks,</p><p>1996). Hence, it is investigated whether or not ANNs can be tted to GARCH data and the possibility that the successfulin-sample results in Kuan and Liu (1995) and Swanson andWhite (1995) are caused by neglected GARCH. A total of1750 data points are generated from</p><p>yt = (ht)1 /2 h th t ~ N(0, 1)</p><p>ht = 0.1 + 0.4ht 1 + 0.4y2t 1where h t and y0 are drawn from the standard normal distri-bution and h0 is set equal to 0.5. The parameters in theANNs are estimated for the yt series for 750 data points, and250 one-step-ahead forecasts are generated; then the sampleis shifted forward 250 observations, and so on. As notedabove, p and q are allowed to be elements of {1, 2, 3, 4, 5},i.e. 25 di erent ANNmodels are considered. The forecastingresults for the GARCH model are summarized in the left-hand side panel of Table 1.At the 5% level, only for one of the 25 cases it is found</p><p>that the corresponding ANN model yields signi cantlymore accurate forecasts. At the 10% level, only four of the25 cases are found with better forecasting performance. It isobserved that the Akaike and Schwarz criteria both selectthe smallest ANN model. If the 25 out-of-sample SRs arecorrelated with the in-sample SRs a correlation coe cientof - 0.110 is obtained, indicating that there is almost nopredictive value of the in-sample t for the out-of-sampleperformance. In sum, this suggests that when the data aregenerated from a GARCH model, there is no evidence thatANNs can yield accurate forecasts, even though linearitytests would sugg...</p></li></ul>


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