forecasting exchange rate better with artificial neural network

Journal of Policy Modeling 29 (2007) 227–236

Forecasting exchange rate better withartificial neural network

Chakradhara Panda a,∗, V. Narasimhan b

a Department of Economics, Faculty of Business and Economics, Addis Ababa University,Addis Ababa, P.O. Box 1176, Ethiopia

b Department of Economics, University of Hyderabad, Central University, Hyderabad 500 046, India

Received 1 May 2005; received in revised form 1 November 2005; accepted 1 January 2006

Abstract

This paper brings into play neural network to make one-step-ahead prediction of weekly Indian rupee/USdollar exchange rate. We also compare the forecasting accuracy of neural network with that of linear autore-gressive and random walk models. Using six forecasting evaluation criteria, we find that neural networkhas superior in-sample forecast than linear autoregressive and random walk models. Neural network is alsofound to beat both linear autoregressive and random walk models in out-of-sample forecasting. This findingprovides evidence against the efficient market hypothesis and suggests that there exists always a possibilityof extracting information hidden in the exchange rate and predicting it into the future. The findings in thestudy have implications for both policy makers and investor’s in the foreign exchange market.© 2006 Society for Policy Modeling. Published by Elsevier Inc. All rights reserved.

JEL classification: C45

Keywords: Feedforward neural network; Training; In-sample prediction; Out-of-sample prediction

1. Introduction

The question “what is the need of forecast of exchange rate at all?” has engrossed many policymakers and economists for many years. The abandonment of Bretton Woods System and theadvent of floating exchange rate system were aimed to empower the monetary authority to conductmonetary policy independent of external imbalances. In the floating exchange rate regime, theexchange rate plays as principal conduit through which monetary policy affects real activity and

∗ Corresponding author.E-mail addresses: [email protected] (C. Panda), [email protected] (V. Narasimhan).

0161-8938/$ – see front matter © 2006 Society for Policy Modeling. Published by Elsevier Inc. All rights reserved.doi:10.1016/j.jpolmod.2006.01.005

mailto:[email protected]

mailto:[email protected]

dx.doi.org/10.1016/j.jpolmod.2006.01.005

228 C. Panda, V. Narasimhan / Journal of Policy Modeling 29 (2007) 227–236

inflation. In order to keep inflation stable at appropriate moderate level and real economic activityat higher level, the monetary authority must have confidence, which will come through the betterunderstanding of the movements of exchange rate of a country, in conducting the monetary policy.The second reason why policy makers watch foreign exchange rate market carefully is becauseexchange rate is a financial asset and thus is potentially valuable source of timely information abouteconomic and financial conditions. Therefore, by understanding the movement of exchange ratebetter, the policy makers will be able to extract the relevant information about the economic andfinancial conditions of the economy. This will enable them to design a better monetary policy forthe future which will in turn achieve its desired objective of price stability and greater employment.

Third, practically most of the countries have managed floating exchange rate system in whichthe central bank restricts the free movement of exchange rates. The intervention from central bankis needed to prevent undesirable or disruptive movements in the exchange rates which cause harmfor internal as well as external sector of the economy. By doing so, the central bank may be ableto bring the desired macro economic stability of the economy. However, in order to interveneefficiently in the foreign exchange market, the policy makers in the central bank must be verymuch aware of the movement of exchange rate and its consequences. Perhaps, these are fewreasons why policy makers might wish to forecast exchange rates. Similarly, firms or investorsmight wish to forecast exchange rates to make asset allocation decisions.

However, the understanding of the movements of exchange rate has become a difficult tasksince the inception of the floating exchange rate system and the liberalization of foreign exchangecontrol. The determinants of exchange rate have grown manifold making its behavior complex,nonlinear and volatile. Indeed, some researchers also believe that modeling the behavior or theprediction of exchange rate is not feasible. They claim that the evolution of any exchange ratefollows the theory of efficient market hypothesis (EMH). Following the hypothesis, it can be saidthat the best prediction value for tomorrow’s exchange rate is the current value of the exchangerate and the actual exchange rate follows a random walk.

The pessimism about the prediction of exchange rate becomes generally accepted after thepublication of the seminal paper by Meese and Rogoff (1983). They indicate that no singleeconomic model of exchange rates is better in predicting bilateral exchange rates during floatingexchange rates than the simple random walk model. However, their results are not surprisingand can easily be explained by the fact that all the models investigated in their work are linear,whereas it is widely agreed that exchange rate movements are nonlinear (Brooks, 1996; Drunat,Dufrenot, Dunis, & Mathiew, 1996; De Grauwe, Dewachter, & Embrechts, 1993; Hsieh, 1989)during floating exchange rates. Hence, it is natural to conjecture that exchange rate data containnonlinearities that cannot be fully accounted for or approximated well by linear models.

One amongst nonlinear models, which has been proposed and examined in recent years forforecasting exchange rates, is artificial neural network (ANN)1 model. In this paper, we use arti-ficial neural network for one-step-ahead prediction of weekly Indian rupee/US dollar (INR/USD)exchange rate. The present paper tries to find answers for there basic questions on empiricalresearch on exchange rates: (i) Is the foreign exchange rate market efficient? (ii) What model bestpredicts exchange rate movements? and (iii) How can we model exchange market participants’expectations. From policy view point, the answer to these questions is of enormous importance.If it can be shown that the foreign exchange market is ‘efficient’ then the case for governmentintervention in that market would be considerably undermined; while if we can identify a model

1 For detailed understanding of ANN, the interested reader may refer Panda and Narasimhan (2003).

C. Panda, V. Narasimhan / Journal of Policy Modeling 29 (2007) 227–236 229

that successfully explains exchange rate determination, it would be possible for the authoritiesto determine the best way to influence exchange rates and limit exchange rate volatility. Further-more, the consequences of alternative economic policy measures could be better evaluated as theirimplications for the exchange rate would be understood. Finally, if we understood how exchangemarket participants form their views on exchange rates, then policy makers may be able to usesuch information to help them in the process of stabilizing exchange rates (Pilbeam, 1998).

To find answers for the questions raised above, we compare the forecasting performance ofneural network with the performances of linear autoregressive (LAR) and random walk (RW)models. The rest of the paper proceeds as follows. In Section 2, we discuss the past studies andin Section 3 we present description of data. Section 4 brings out the model selection proceduresfor neural network, linear autoregressive and random walk models. In Section 5, we present theempirical findings. Finally, Section 6 concludes the paper with policy implications.

2. Previous works

Neural network has some advantages over other linear and nonlinear models which make itattractive in financial modeling. First, neural network has flexible nonlinear function mappingcapability which can approximate any continuous measurable function with arbitrarily desiredaccuracy (Cybenko, 1989; Hornik, Stinnchcombe, & White, 1989), whereas most of the commonlyused nonlinear time series models do not have this property. Second, being nonparametric anddata-driven model, neural network imposes few prior assumptions on the underlying process fromwhich data are generated. Because of this property, neural network is less susceptible to modelmisspecification problem than most parametric nonlinear methods. This is an important advantagesince exchange rate does not exhibit a specific nonlinear pattern. Third, neural network is adaptivein nature. The adaptivity implies that the network’s generalization capabilities remain accurate androbust in a nonstationary environment whose characteristics may change over time. Fourth, neuralnetwork model uses only linearly many parameters, whereas traditional polynomial, spline, andtrigonometric expansions use exponentially many parameters to achieve the same approximationrate (Barron, 1991).

Given the advantages of neural network, it is not surprising that this methodology has attractedoverwhelming attention in exchange rate prediction. Kuan and Liu (1995) find that neural networkis able to improve the sign predictions and its forecasts are always better than the random walkforecasts. Gencay (1999) compares the performance of neural network with those of random walkand GARCH models in forecasting daily spot exchange rates for the British pound, Deutschemark, French franc, Japanese yen, and the Swiss franc. He finds that forecasts generated byneural network are superior to those of random walk and GARCH models. Wu (1995) conductsa comparative study between neural networks and ARIMA models in forecasting the Taiwan/USdollar exchange rate. His findings show that neural networks produce significantly better resultsthan the best ARIMA models in both one-step-ahead and six-step-ahead forecasting. Similarly,Hann and Steurer (1996) and Zhang and Hu (1998) find results in favor of ANN. However, onthe other hand, Plasmans, Verkooijen, and Daniels (1998); Verkooijen (1996) do not producesatisfactory monthly forecasts of exchange rates using ANN.

3. Description of data

This paper studies the weekly spot rates of Indian rupee/US dollar (INR/USD) exchange rate.The data set is from FX database for the period of January 6, 1994–July 10, 2003, for a total


Table 1Summary statistics for the weekly exchange rates: log first difference January 6, 1994–July 10, 2003

Description INR/USD

Sample size 496Mean 0.0455Median 0.0052S.D. 0.2806Skewness 2.4834Kurtosis 42.5818Maximum 3.1904Minimum −1.7316Jarque-Bera 32888 (0.000)ρ1 0.131ρ5 −0.002ρ10 −0.008ρ15 0.080ρ20 −0.059LB statistic (20) 42.34 (0.000)ADF −9.348

Note: The p-value for Jarque-Bera and LB statistic is given in parentheses. The MacKinnon critical values for ADF testare −3.98, −3.42, and −3.13 at 1%, 5%, and 10% significance level, respectively.

497 observations. The weekly returns are calculated as the log differences of the levels. Let pt

be the exchange rate price for the period t. Then the exchange rate return at time t is calculatedas yt = (log(pt) − log(pt−1)) × 100. We multiply the log difference by 100 to reduce round-offerrors. Table 1 presents the summary statistics of the data. Both the skewness and kurtosis aresubstantially high. The kurtosis coefficient, i.e. 42.5818, is larger than that of the standard normaldistribution (which is equal to 3), which in turn indicates the leptokurtosis of INR/USD returnseries. Jarque-Bera statistic also rejects the normality of exchange rate, which is common in highfrequency financial time series data. The first 20 autocorrelations are calculated but only fiveautocorrelations i.e. ρ1, ρ5, ρ10, ρ15, ρ20 are reported in the table. The series shows evidenceof autocorrelation. The Ljung-Box (LB) statistic for the first 20 lags is 42.34, which rejects thehypothesis of identical and independent observations. The value for Augmented Dicky-Fuller(ADF) test statistic confirms the stationarity of weekly exchange rate return series.

4. Model selection

In this section, we discuss model selection procedure for neural network, linear autoregressiveand random walk models. In neural network, model selection i.e. selection of optimal neuralnetwork architecture is a daunting task. Failures of neural network in some applications aresometimes due to sub optimal network structure. In this paper, however, we believe that experimentis the best teacher. Thus, the number of inputs and hidden units are chosen through systematicexperimentation. We keep 350 observations for training (i.e. in-sample data) and remaining 146observations are kept for testing (i.e. out-of-sample data). We normalize the data to the valuebetween 0 and 1. A single-hidden-layer feedforward network is used for the training in whichsigmoid transfer function is used in the hidden layer and linear transfer function is used in theoutput layer. The weights are initialized to small values based on the technique of Nguyen andWidrow (1990) and mean square error is the taken as the cost function in our study. We train


the network by using resilient backpropagation algorithm. These are all standard choices in theneural network.

As mentioned earlier, the number of input nodes and hidden nodes to the network are selectedthrough experimentation. The number of input nodes, in this work, corresponds to the number oflagged past observations. Thus, the resulting network is a nonlinear autoregressive model, whichplays an important role in determining the autocorrelation structure of a time series. Twentylevels of the number of input nodes ranging from 1 to 20 lagged values of the dependent variablei.e. weekly exchange rate returns are used in this study. However, we only experiment with fivelevels of hidden nodes 4, 8, 12, 16, and 20 across each level of input node by following previousfindings (see, Zhang and Hu (1998) and Hu, Zhang, Jiang, and Patuwo (1999)) that the forecastingperformance of neural networks is not as sensitive to the number of hidden nodes as to the numberof input nodes.

The effects of input nodes and hidden nodes on neural network training performance areshown in Table 2. The root mean square errors (RMSEs) in the table, at each level of input nodein combination with each five hidden node are the average of 10 runs. The results show that asthe number of input nodes increases, except for input nodes 6, 12, 13, and 15, RMSE decreasesas reflected by the average of RMSEs across the five hidden node levels at each level of the inputnode. Hence, we drop the input nodes 6, 12, 13, and 15 from the vector of input nodes and useother 16 input nodes to forecast the weekly exchange rate return. The simple reason is that thedropped variables do not contribute anything to explain the behaviour of the exchange rate returnas reflected by the increasing average RMSEs at these input levels across five hidden nodes levels.The results also show that RMSE decreases as the number of hidden nodes increases at each levelof input node except for input nodes 8, 10, 11, 15, 17, 19, and 20. More over, we do not find a clearhidden node effect. Because of these findings, we could not settle down at a specific optimumhidden node. We try with more than one hidden layer combined with different hidden nodes. Aftertrying several combinations, we find two hidden layers with three hidden units in each layer asthe best combination. Hence, the optimal neural network architecture i.e. 16-3-3-1 is to be usedfor the in-sample and out-of-sample forecasting of weekly exchange rate return.

Next, we discuss the model specification of linear autoregressive and random walk models.In linear autoregressive model, to select the optimum autoregressive terms, we first regress thedependent variable yt on a large group of independent variable. We take the first 20 lagged valuesof the dependent variable i.e. from yt−1 to yt−20 as explanatory variables. Then a small groupof statistically significant variables are identified and used as explanatory variables to forecastweekly exchange rate return. From regression results,2 we find that among all 20 lags, lags 1, 4, 6,7, 15, and 19 are found to be significant. These significant lags are used as explanatory variablesfor the problem of forecasting weekly exchange rate return. As far as the model specification ofrandom walk is concerned, we do not estimate any model. We simply take random walk withoutdrift, which says of no change in forecasting. By virtue of this, current period’s value is consideredas the best predicting value for tomorrow.

5. Empirical findings

After selecting the appropriate models for neural network, linear autoregressive and randomwalk, we next turn to see the forecasting power of all three studied models. In Section 5.1,

2 Regression results can be obtained from author on request.


Table 2Effects of neural network factors on the training performance

Input Hidden RMSE Input Hidden RMSE

1 4 0.0522 8 4 0.03751 8 0.0508 8 8 0.03421 12 0.0508 8 12 0.03301 16 0.0492 8 16 0.03041 20 0.0485 8 20 0.0294

Avg. 0.0503 Avg. 0.03292 4 0.0493 9 4 0.03772 8 0.0450 9 8 0.03262 12 0.0434 9 12 0.02962 16 0.0434 9 16 0.02902 20 0.0412 9 20 0.0292

Avg. 0.0446 Avg. 0.03163 4 0.0417 10 4 0.03513 8 0.0418 10 8 0.03403 12 0.0397 10 12 0.02693 16 0.0382 10 16 0.02853 20 0.0375 10 20 0.0266

Avg. 0.0397 Avg. 0.03024 4 0.0432 11 4 0.03554 8 0.0370 11 8 0.02874 12 0.0347 11 12 0.02834 16 0.0343 11 16 0.02904 20 0.0341 11 20 0.0274

Avg. 0.0366 Avg. 0.02975 4 0.0410 12 4 0.03325 8 0.0353 12 8 0.03095 12 0.0333 12 12 0.02985 16 0.0317 12 16 0.02785 20 0.0311 12 20 0.0279

Avg. 0.0344 Avg. 0.02996 4 0.0422 13 4 0.03576 8 0.0343 13 8 0.03066 12 0.0340 13 12 0.02886 16 0.0314 13 16 0.02816 20 0.0309 13 20 0.0281

Avg. 0.0345 Avg. 0.03027 4 0.0418 14 4 0.03887 8 0.0329 14 8 0.02787 12 0.0311 14 12 0.02767 16 0.0315 14 16 0.02707 20 0.0300 14 20 0.0254


Table 2 (Continued )

Input Hidden RMSE Input Hidden RMSE

Avg. 0.0334 Avg. 0.029315 4 0.0349 18 4 0.028415 8 0.0278 18 8 0.027715 12 0.0258 18 12 0.024415 16 0.0263 18 16 0.024115 20 0.0249 18 20 0.0238

Avg. 0.0349 Avg. 0.025616 4 0.0292 19 4 0.028416 8 0.0270 19 8 0.025916 12 0.0262 19 12 0.024316 16 0.0260 19 16 0.023716 20 0.0255 19 20 0.0248

Avg. 0.0268 Avg. 0.025417 4 0.0303 20 4 0.028817 8 0.0272 20 8 0.025217 12 0.0246 20 12 0.023517 16 0.0262 20 16 0.023617 20 0.0254 20 20 0.0252

Avg. 0.0267 Avg. 0.0252

Note: The RMSEs at each level of input node in combination with each five hidden node levels are the average of 10 runs.

in-sample forecasts are presented, followed by out-of-sample forecasts in Section 5.2. Six per-formance criteria such as root mean square (RMSE), mean absolute error (MAE), mean absolutepercentage error (MAPE), Pearson correlation coefficient (CORR), direction accuracy (DA)3 andsign predictions (SIGN)4 to evaluate the predictive power of neural networks in comparison tolinear autoregressive and random walk models.

5.1. In-sample forecasts

In-sample performance of neural network, linear autoregressive and random walk models ispresented in Table 3. The results show that neural network outperforms both linear autoregressiveand random walk model by all the evaluation criteria. The RMSE of ANN i.e. 0.2048 is signif-icantly lower than the RMSEs of LAR and RW model which are equal to 0.2518 and 0.3325,respectively. Neural network has also got smaller values for MAE and MAD as compared to thevalues of linear autoregressive and random walk models. The neural network fitted values havehigher correlation, which is equal to 0.6687, with the actual series as compared to the values oflinear autoregressive (0.4062) and random walk model (0.2720). The most important evaluationcriteria, from investor’s point of view, are direction accuracy and sign prediction. Because an

3 DA = 1

N

N∑i=1

ai where ai ={

1 if(yi+1 − yi)(yi+1 − yi) > 0

0 otherwise.

4 SIGN = 1

N

N∑i=1

bi where bi ={

1 if yi+1yi+1 > 0

0 otherwise.


Table 3In-sample performance of the neural network, linear autoregressive and random walk models on weekly exchange ratereturn series

ANN LAR RW

RMSE 0.2048 0.2518 0.3325MAE 0.1057 0.1341 0.1577MAPE – – –MAD 0.0379 0.0519 0.0540CORR 0.6687 0.4062 0.2720DA 0.6848 0.6424 0SIGN 0.5181 0.5030 0.5030

investor is more enthusiastic to know about the directional and sign change in the exchange ratereturn for tomorrow rather than the exact magnitude of it. In the Table 3, we can see that neu-ral network gives better sign predictions than linear autoregressive and random walk model. Itcan also be seen that neural network’s direction accuracy of ANN, which is equal to 0.6848, ishigher than the corresponding value of LAR (0.6424). Here it should be noted that the directionaccuracy is zero for random walk. This is because, by definition, the random walk has abso-lutely no ability to predict whether the exchange rate return will go up or down since it simplytakes the exchange rate return of current period as the forecast of the next period and predicts nochange.

5.2. Out-of-sample forecasts

The results for out-of-sample performance are presented in Table 4. The out-of-sample fore-casts of neural network and linear autoregressive models are more accurate than random walkforecasts by all criteria except for the Pearson correlation coefficient. The correlation coefficientfor ANN and LAR are 0.1851 and 0.2201, respectively, as compared with the corresponding figureof random walk, which is equal to 0.2535. The superiority of neural network and linear autoregres-sive over random walk in out-of-sample forecasts provides evidence against the efficient markethypothesis. However, between neural network and linear autoregressive model, neural networkhas superior out-of-sample results when RMSE, MAE, MAD, and DA are considered as evalu-ation criteria. The values of RMSE, MAE, and MAD for ANN are 0.1087, 0.0676, and 0.0318,respectively. The corresponding values for LAR are 0.1096, 0.0740, and 0.0350, respectively. Theneural network has higher direction accuracy, which is equal to 0.7063, than linear autoregressive

Table 4Out-of-sample performance of the neural network, linear autoregressive and random walk models on weekly exchangerate return series

ANN LAR RW

RMSE 0.1087 0.1096 0.1342MAE 0.0676 0.0740 0.0854MAPE – – –MAD 0.0318 0.0350 0.0474CORR 0.1851 0.2201 0.2535DA 0.7063 0.5793 0SIGN 0.5714 0.6031 0.5634


model (0.5793). On the other hand, linear autoregressive model outperforms neural network interms of correlation coefficient and the percentage of correct sign prediction.

6. Summary and policy implications

In this paper, we use neural network as an alternative forecasting technique to linear autore-gressive and random walk models in the one-step-ahead prediction of weekly Indian rupee/USdollar exchange rate. Our findings suggest that neural network has superior in-sample forecastthan linear autoregressive and random walk models. As far as the out-of-sample forecasting isconcerned, neural network outperforms random walk by all evaluation criteria, except for Pearsoncorrelation coefficient. Neural network is also found to beat linear autoregressive model by fourout of six evaluation criteria in out-of-sample forecasting.

The findings of this paper have following policy implications. First, the superiority of artifi-cial neural network over random walk model suggests that the foreign exchange market is notefficient. There always exists a possibility of forecasting exchange rate. The better forecasting orunderstanding of the movements of exchange rate by using artificial neural network may help thepolicy makers to conduct a suitable monetary policy which will in turn achieve its desired objec-tives of price stability and higher economic activity. Second, the better forecast of exchange rateby neural network over liner autoregressive model recommends that the linear unpredictabilityof exchange rate can be improved and nonlinearities can be captured by using a nonlinear modellike neural network.

Third, the superiority of neural network over both linear autoregressive and random walkmodels show that the information that are hidden in exchange rate can be better extracted byusing artificial neural network. This finding also indicates that the exchange market participants’expectations are better modeled by neural network. Therefore, the use of neural network mayhelp policy makers in extracting useful information about the economic and financial conditions.Finally, firms or investors in the foreign exchange market can usefully apply artificial neuralnetwork in predicting exchange rate for the future and thus can take a profitable trading strategyand a proper decision on asset allocation. We believe, we have answered all three questions raisedat the beginning of the paper.

Acknowledgement

The authors gratefully acknowledge University Grants Commission (UGC), Government ofIndia, for the financial support.

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