predicting exchange rates using a novel “cointegration based neuro-fuzzy system”

Contents lists available at ScienceDirect

International Economics

International Economics 137 (2014) 88–103

2110-70Internathttp://d

n CorrE-m

journal homepage: www.elsevier.com/locate/inteco

Predicting exchange rates using a novel “cointegrationbased neuro-fuzzy system”

Behrooz Gharleghi a,n, Abu Hassan Shaari b, Najla Shafighi b

a Faculty of Business and Management, Asia Pacific University of Technology and Innovation, TPM, Bukit Jalil,57000 Kulala Lumpur, Malaysiab Faculty of Economics and Management, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia

a r t i c l e i n f o

Available online 18 December 2013

Jel classification:E47F31F37

Keywords:Exchange rateError correction modelIntelligence systemsNeural networksUnit root

17/$ - see front matter & 2013 CEPII (Centreionales), a center for research and expertisex.doi.org/10.1016/j.inteco.2013.12.001

esponding author. Tel.: +60 196153515; faxail address: [email protected] (B. Gh

a b s t r a c t

The present study focuses upon the applications of currentlyavailable intelligence techniques to forecast exchange rates in shortand long horizons. The predictability of exchange rate returns isinvestigated through the use of a novel cointegration-based neuro-fuzzy system, which is a combination of a cointegration technique;a Fuzzy Inference System; and Artificial Neural Networks. TheRelative Price Monetary Model for exchange rate determinationis used to determine the inputs, consisting of macroeconomicvariables and the type of interactions amongst the variables, inorder to develop the system. Considering exchange rate returns ofthree ASEAN countries (Malaysia, the Philippines and Singapore),our results reveal that the cointegration-based neuro-fuzzy systemmodel consistently outperforms the Vector Error Correction Modelby successfully forecasting exchange rate monthly returns with ahigh level of accuracy.

& 2013 CEPII (Centre d’Etudes Prospectives et d’InformationsInternationales), a center for research and expertise on the world

economy Published by Elsevier Ltd. All rights reserved.

1. Introduction

The foreign exchange market is the largest and most liquid of financial markets. The issue of whetherexchange rates are linear or non-linear remains controversial (Brooks, 1996; Satchell and Timmermann,

d’Etudes Prospectives et d’Informationson the world economy Published by Elsevier Ltd. All rights reserved.

: +60 389961001.arleghi).

www.elsevier.com/locate/inteco

www.elsevier.com/locate/inteco

http://dx.doi.org/10.1016/j.inteco.2013.12.001



mailto:[email protected]


B. Gharleghi et al. / International Economics 137 (2014) 88–103 89

1995; Zhang et al., 1998; Khashei et al., 2009; Zhang and Hu, 1998). However, empirical internationalfinance literature demonstrates a growing interest in nonlinear models of exchange rate behavior(Clements and Yihui, 2010; Yu et al., 2005; Leung et al., 2000). Hence, efforts to predict exchange ratesbeyond monthly horizons remain a worthwhile endeavor. Forecast modeling continues to have greatimportance in the field of economics and is widely applied in various other fields.

Exchange rate return forecasting is a highly complicated and arduous task because many factorsexist that may influence exchange rates, including relative price levels, balance of payments, interestrates, risk, real income, economic growth, government expenditure and other economic factors (Isard,1980; Hopper, 1997; Kia, 2013). Furthermore, exchange rate series are generally nonlinear, dynamic,noisy, complicated, chaotic, and nonparametric in nature, as demonstrated in Yudong and Lenan(2009). The present study examines exchange rate predictions that are obtained using a cointegration-based neuro-fuzzy system. The predictions are premised upon data collected in regards to exchangerates in Malaysia, the Philippines and Singapore. In order to strengthen the constructed system andimprove the output, the Relative Price Monetary Model (RPMM) (Balassa, 1964; Samuelson, 1964;Chinn, 1998) for exchange rate determination is used. The RPMM is tested using the Johansen–Juseliuscointegration technique (J–J test) in order to determine the long-run relationship between theexchange rate series and the selected macroeconomic variables. The principal contribution of thepresent paper is a cohesive presentation and classification of soft computing techniques applied toselected ASEAN exchange rates that may be used for further analysis and evaluation; and futurecomparative studies. An obvious benefit of the present study is that the results obtained under thecointegration-based neuro-fuzzy system may offer additional information regarding market behavior.Exchange rate forecasters focus on developing approaches to successfully predict exchange rate priceswith the ambit of maximizing profits. The success of a model utilized for the purpose of exchange rateprediction is effectively premised upon the accuracy of the results; the minimization of requiredinputs; and the reduction of the complexity of the model itself.

The cointegration-based neuro-fuzzy system developed in the present paper is constructed basedupon the following procedure and techniques. First, the cointegration technique is implemented usingRPMM to determine the long-run relationship among the variables, as well as the sign of long-runcoefficients. Second, once the presence of cointegrating vectors is demonstrated, the sign of coefficientsin the long-run equation is used to construct the fuzzy inference system (FIS). Finally, the generatedfuzzy inference system produces the values required for the artificial neural network (ANN) to predictthe exchange rate. Therefore, the present investigation can be distinguished from extant studies on twoprincipal bases. First, in this paper, the neuro-fuzzy system is constructed based upon a cointegrationapproach, whereas neuro-fuzzy systems in extant studies are constructed without taking cointegrationamong the variables into account (Tahmasebi and Hezarkhani, 2010; Atsalakis and Valavanis, 2009b;Esfahanipour and Aghamiri, 2010; Boyacioglu and Avci, 2010; Liang et al., 2011). Second, the neuro-fuzzysystem considered here is not adaptive since the rules do not change while the system is trained, unlikethe commonly applied adaptive neuro-fuzzy inference system (ANFIS) where rules are adapted. Ourempirical results indicate a unique cointegrating vector for all three currencies, as well as a significantimprovement in prediction results using the cointegration based neuro-fuzzy system.

The remainder of the paper is organized as follows. Section 2 outlines the extant literature, whileSection 3 introduces the basic theory underlying the cointegration approach, the FIS and ANNs.Section 4 describes the data, and our empirical findings are presented in Section 5. Section 6concludes the paper.

2. Previous studies

The exchange rate forecastability puzzle suggests that macroeconomic fundamentals containa negligible predictive content about the movements of nominal exchange rates. Since the seminalpapers by Meese and Rogoff (1983a, 1983b) and numerous scholars have attempted to refinetheoretical models or improve estimation techniques to explicate the puzzle (Mark, 1995; Manzan andWesterhoff, 2007; Sarmidi, 2010). However, the empirical evidence consistently fails to overturn this

B. Gharleghi et al. / International Economics 137 (2014) 88–10390

paradox. Consequently, clarifying the exchange rate predictability puzzle remains a challenging areafor contemporary researchers.

ANNs have been successfully applied when solving problems associated with financial time seriesforecasting, including exchange rates and financial stock markets (Md Nor and Gharleghi, 2011;Armano et al., 2005; Egeli et al., 2003; Hiemstra, 1995; Karaatli et al., 2005; Leigh and Purvis, 2002;Manish and Thenmozhi, 2006; Saad et al., 1998; Khashei and Bijari, 2010; Yudong and Lenan, 2009). Inlight of the desire for better techniques, numerous extant studies focus on the prediction of exchangerates using neuro-fuzzy systems. For instance, neuro-fuzzy systems are utilized by Alakhras (2005) forthe exchange rate in Turkey; by Kablan (2009) in relation to the EUR/USD exchange rate; by Changand Liu (2008) for the Taiwan stock exchange; by Gradojevic (2007) in relation to the daily currencytrading rule; and by Kodogiannis and Lolis (2001) for the British Pound/USD exchange rate.

Quek (2005) applies the ANFIS to forecast investors' measures in the stock exchange trading in theUnited States. Generally, these techniques are considered to successfully predict stock prices in the USstock exchange market and other stock markets, such as the Tehran stock exchange (Abbasi andAbouec, 2008) and the Taiwan stock exchange (Long et al., 2010). Similarly, neuro-fuzzy systems arealso successfully applied in predicting exchange rate markets in the cases of the Euro/USD exchangerate (Kablan, 2009); and exchange rates in Turkey (Alakhras, 2005). Trinkle (2006) applies the ANFIS,neural network, and autoregressive integrating moving average (ARIMA) model when forecasting theannual excess returns of three publicly traded companies. The forecasting performance of the twointelligence techniques is compared against the ARIMA model. The results reveal that the ANFIS andneural network techniques have significant prediction abilities over the ARIMA model. Yunos et al.(2008) develop an ANFIS to forecast the daily movements of the Kuala Lumpur Composite Index(KLCI). Four technical criteria are chosen to evaluate the performance of the models. The resultsindicate that the ANFIS utilized is competent in forecasting the KLCI as compared to ANNs.

Ang and Quek (2006) propose a novel rough set-based neuro-fuzzy stock trading decision model,referred to as the stock trading using Rough Set-Based Pseudo Outer-Product (RSPOP), whichsynergizes the price difference forecast method with a forecast bottleneck free trading decisionmodel. The performance of Ang and Quek model is compared to (i) the dynamic evolving neural-fuzzyinference system (DENFIS) forecast model; (ii) the stock trading without forecast model; and (iii) thestock trading with ideal forecast model. The empirical results reveal that the proposed modelidentified rules with greater interpretability and yielded significantly higher profits than the stocktrading with DENFIS forecast model and the stock trading without forecast model. Keles et al. (2008)also apply a neuro-fuzzy model to forecast domestic debt. Fuzzy logic offers better insight comparedto neural networks, but its performance depends on the fuzzification of the time series data. Atsalakisand Valavanis (2009b) develop a neuro-fuzzy adaptive system to forecast the one step ahead of stockprice trends for the ASE and the NYSE indices. Their results reveal that the proposed model performsvery well in trading simulations. Kodogiannis and Lolis (2001) perform a comparative analysis ofneural networks and fuzzy systems for one-step-ahead prediction of the GBP/USD daily exchange rate.Their proposed hybrid learning algorithms provided a new dimension to exchange rate prediction.The advantages of their proposed model are the inclusion of an innovative defuzzification method;the ability of the model to learn from experience; and a high computation rate. Ucenic and Atsalakis(2009) utilize an ANFIS forecasting model and showed that, based upon the root mean squared error(RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE), the ANFIS modelgives the best results when six gauss membership functions and 300 epochs (number of iterations)are employed.

None of the extant studies referred above, however, rely on a cointegration method in thedevelopment of the FIS. We fill this gap in the present study.

3. Methodology

Since the present paper introduces a model combining three different techniques to achieve higheraccuracy in prediction, the techniques are presented below to highlight the procedures involved inthe new system construction. A cointegration test determines the long-run interactions between the


exchange rates and the macro-variables using RPMM. The sign of the coefficients in the long-runequation is used to construct the FIS; the latter being based upon the economic theory of exchangerate determination (i.e., RPMM). The results from the FIS are utilized as inputs for the ANN to predictthe exchange rate returns.

3.1. Cointegration tests

The J–J test (Johansen and Juselius, 1990) is well known and used in applied econometrics. Thecointegration technique examines whether a common trend exists within a set of variables where thestochastic trend in one variable is related to the stochastic trend in some other variable(s). The J–J test isutilized to determine whether cointegration exists among the variables. The Johansen (1988) cointegrationanalysis involves the estimation of the following reduced form of vector autoregressive model:

Δzt ¼ ∑k

i ¼ 1ΓtΔzt� iþΦzt�1þΨdþεt ð1Þ

where zt is a vector of non-stationary variables. The matrix Φ has reduced rank equal to r and can bedecomposed toΦ¼α'β, where α and β are p� r full rank matrices and represent adjustment coefficients andcointegrating vectors, respectively. d is the vector of deterministic variables, which may include constantterm, linear trend, seasonal dummies and impulse dummies. The error term is normal and independentlydistributed. In order to determine the number of cointegration relationships among the variables, the J–J testincludes two different tests: the Trace test and Maximum Eigenvalue test. In the trace test, the nullhypothesis assumes that there are at most r cointegrating vectors and the hypothesis is tested against ageneral alternative. In the maximum eigenvalue test, the null hypothesis of r cointegrating vectors isexamined against rþ1 cointegrating vectors (Johansen, 1991). When the cointegrating vectors among thevariables are identified, then the sign of the coefficients from the long-run equations are used for thedevelopment of the FIS.

3.2. Fuzzy inference system

Fuzzy logic was introduced by Zadeh (1965) and provides a solution to extract the desired resultsfrom insecure (undetermined) and weak information. Fuzzy logic is more applicable, successful andaccurate in modeling situations where estimation cannot be performed by other common methods.Therefore, in such situations, the determination of fuzzy rules and fuzzy membership functions arenot easy. To assist in the determination of such rules and functions, theory relevant to the topic underconsideration is inherently useful. Fuzzy logic has three distinct steps that must be followed:(i) fuzzification, which refers to numerical values in the real world that are transformed into fuzzyconcepts or linguistic variables; (ii) aggregation, which includes the calculation of fuzzy valuesbetween zero and one; and (iii) defuzzification, which involves the transformation of the linguisticvariables in the fuzzy system into numerical values in real world. Fuzzy systems are non-linear,adaptive and include expert knowledge, which can be easily used for complex and nonlinear patterns.

In the present study, the Mamdani FIS is applied to generate the results. The system proposed byMamdani (1974) is developed in an attempt to control a steam engine and boiler combination bysynthesizing a set of linguistic control rules obtained from experienced human operators. Mamdani'sefforts are based on Zadeh's paper concerning fuzzy algorithms for complex systems and decisionprocesses. The Mamdani FIS suggests the output of membership functions to be a fuzzy set. Theadvantages of the Mamdani FIS are, first that the FIS can consider the uncertainty and imprecisenessimposed during the experimentation. This method is commonly used for the practitioners torepresent model inputs in linguistic terms like, high, low, medium rather than representing inquantitative terms. Second, the permission for attachment properties allows the researcher to obtainfewer complex models without loss of accuracy.

The manner in which the FIS functions is presented in Fig. 1. The crisp input is transformed intofuzzy input by fuzzification. The fuzzy values are formulated by identifying the uncertaintiespresented in the crisp values. The transformation of fuzzy values is represented by the membership

Fig. 1. Fuzzy inference system.


functions. Fuzziness in a fuzzy set is characterized by its membership functions, which classify theelements in the set for both discrete and continuous. The “shape” of the membership function is animportant criterion to consider. Various types of membership functions exist, including trapezoidal,triangular and Gaussian distribution. The membership function shows the degree of membership to alinguistic variable or fuzzy set. For example, in Fig. 3, when the exchange rate is 4.2, the rate can beperceived as being very high or extremely high depending upon the membership function. Afterfuzzification, the rule base components are created, which contain the rules that are defined for thesystem based on cointegration results. The rule base and the database (actual data) are collectivelyreferred to as the knowledge base. The decision-making is a major part in the entire system. The FISforms suitable rules and the decision is made based upon the rules formulated. Finally, defuzzificationprocess is performed, which is a process utilized to transform the fuzzy values into a crisp values.Fuzzy values cannot be directly applied in modeling because they are linguistic values. Therefore, thetransformation of fuzzy values into crisp quantities is required for further processing. The resultingcrisp values are the actual output of a fuzzy inference system.

The developed FIS is a combination of rules (based on cointegration results) and data given to thesystem. Therefore, the generated results from the FIS are more accurate than the raw data. Theseresults become the necessary inputs for the ANN to predict the exchange rate.

3.3. Artificial neural networks

ANNs are a type of modeling method based upon the human brain that recognize and learn therules based upon the past data provided; and saves and applies the rules to future data. ANNs areappropriate methods to forecast the exchange rate due to some unique features. First, ANNs are self-adaptive in that few assumptions are utilized in the models. Second, in relation to generalizationability, ANNs can infer the unseen part of population even if the sample data contains noisyinformation. Third, ANNs are non-linear and, finally, ANNs are universal functional estimators, whichmean that neural networks can estimate any continuous function to any desired accuracy (Khasheiet al., 2008). The great advantage of neural networks is their flexibility in modeling nonlinear patterns.When utilizing ANNs, no need exists to specify any particular model because ANNs can be adapted tothe features presented in the data set, which is commonly referred to as a data driven approach. Suchan approach is useful for empirical researches where no theoretical guidelines are available to suggestan appropriate data generating process (Md Nor et al., 2011).

The feed forward neural network (FFNN) is the most commonly used neural network in which alllayers, except the input layer, receive weights from their previous layer. This type of neural networkconsists of three layers: the input layer, which includes the explanatory variables (inputs) utilized inthe model; the output layer, which includes the output of the network; and the hidden layer, whichlies between the input and output layers. A sufficient number of hidden layers in a FFNN allow thenetwork to learn, adjust and generalize based upon previously learned facts (data sets) to the newinput. The number of hidden layers and nodes in the network are determined by trial and error, atechnique which is adhered to in the present study.


A single hidden layer FFNN for time series modeling and forecasting, consisting of three layers ofsimple processing units connected by acyclic links, is represented as follows:

yt ¼w0þ ∑q

j ¼ 1wj�g w0;jþ ∑

p

i ¼ 1wi;j�yt� i

!þεt ð2Þ

where wi,j (i¼0,1,2,…,p, j¼1,2,…,q) and wj (j¼0,1,2,…,q) represent connection weights; p is thenumber of input nodes; q is the number of hidden nodes and εt is the random error term. Fig. 2represents the simple structure of a FFNN:

From the figure, it can be seen that four neurons are present in the input layer; five neurons arepresent in the hidden layer; and one neuron is present in the output layer. Neurons must utilizeactivation functions to generate the output. An activation function represents a degree of nonlinearity,which is valuable for neural network applications. The activation function is specified by the situationof the neuron within the network and can take several forms. The most commonly used activationsfunctions in hidden layer transfer functions are (i) the sigmoid activation function; (ii) the tangenthyperbolic activation function; and (iii) the Tansig activation function, which is a combination of both(i) and (ii). The present study utilizes the Tansig activation function, which is represented as follows:

TansigðnÞ ¼ 2ð1þe�2nÞ �1 ð3Þ

A FIS can replicate human expertise by storing essential components in a rule base and performing fuzzyreasoning to infer the overall output value. The derivation of IF-THEN rules and correspondingmembership functions depends on a priori knowledge of the system. On the other hand, ANN learningmechanisms do not rely on human expertise due to the homogenous structure of ANNs. The combinationof FIS and neural networks provides a strong tool for prediction, which reflects the advantages of humanexpertise in FIS and the advantages of the learning algorithms in neural networks (Vieira et al., 2004).

4. Data

Theoretically, exchange rate returns appear to be based on the macroeconomic variables. As such,the RPMM of exchange rate determination is applied, which incorporates macroeconomic variablesinto the model. The macroeconomic variables that determine the behavior of exchange rates in theRPMM are money supply, national income, interest rate, inflation rate, customer price index andproducer price index (Frenkel, 1976, 1979; Dornbusch, 1976; Meese and Rogoff, 1983a). As such, thesevariables are included as inputs in the system constructed in the present study. M2 is utilized as arepresentative for money supply, while the industrial production index (IPI) is used as a proxy fornational income due to the lack of availability of monthly data for gross domestic product.Additionally, the federal fund rate is used for interest rate. All other variables are used as presentedabove. The dependent variable is the monthly return of the exchange rates against the USD.

Fig. 2. Structure of a three layers feed forward neural network.


Macroeconomic variables; and the Malaysian Ringgit (MYR), Philippine Peso (PHP) and SingaporeanDollar (SGD) exchange rates against the USD are collected from the International Financial Statistics database. The data are of monthly frequency and span from 1998 (M01) to 2010 (M09). The dataset includesa total of 153 observations for each variable and is divided into two parts. The first group of data (141observations) is utilized for training purposes, while the second group (12 observations) is utilized forprediction purposes. All variables are expressed in log form and the return of exchange rate is calculatedas follows:

et ¼ log ðexrt=exrt�1Þ ð4Þ

where e is the return of exchange rate and exr is the real exchange rate.

5. Empirical findings

This section presents the empirical results of the present study. The structure of the presentation ofthe results follows the sequence of methodologies employed in the present paper and thereforebegins with the cointegration results used to construct the FIS. Later, the initial findings from the FISare presented, followed by a presentation of the cointegration-based neuro-fuzzy system predictionresults.

5.1. Cointegration results

The Augmented Dickey Fuller (ADF) and the Philips-Perron (PP) unit root tests are applied to theselected Malaysian macroeconomic variables and indicate that the variables are stationary at firstdifference. Although IPI shows stationarity at level-intercept using the ADF test, the final conclusion isin favor of first order of integration. A conclusion in favor of the null hypothesis can only result in theevent that both the ADF and the PP tests fail to reject the null hypothesis. Philippine macroeconomicvariables are stationary at first difference. Even though IPI and money supply show stationarity atlevel-trend-intercept using the ADF test, the final conclusion is in favor of first order of integration.Singaporean macroeconomic variables are also integrated of order one even though the IPI showsstationarity at level-trend-intercept using the ADF test. The results obtained from integration testssuggest the possibility of a long-run relationship among the variables; therefore, J–J test is performed.Unit root results are presented in Appendix A.

The J–J-test, including the trace and maximum eigenvalue tests, points to one cointegratingrelationship for all three currencies. Both the trace and maximum eigenvalue tests affirm the presenceof a long-run equilibrium relationship between the variables. This indicates that all variables usedin the model are significant and should be used in the neuro-fuzzy system. Long-run coefficientsare used to determine the type of interactions between the macro variables and exchange rate.The implied long-run coefficients from the estimated cointegrating vector, which are normalized onthe exchange rate, are used to construct the neuro-fuzzy system. The results for the cointegration testsare presented in Tables 1–3, for Malaysia, the Philippines and Singapore, respectively.

From the tables, it can be seen that money supply and interest rate have a direct relationship withthe exchange rate, while national income, inflation rate and relative price variable have an inverserelationship with exchange rates in long-run. In the case of the Philippines (Table 2), money supply,inflation and relative price variables have an inverse relationship with the exchange rate, whilenational income and interest rate have a direct relationship with the exchange rates examined. Finally,in the case of Singapore (Table 3), national income and inflation have a direct relationship with theexchange rate, while money supply, interest rate and relative price variables have an inverserelationship with the exchange rates examined. Interestingly, the sign of the relative price variable isconsistent in all countries. From the results obtained from the long-run coefficients and their relatedsigns, the rules of the developed neuro-fuzzy system are derived and constructed. The neuro-fuzzysystem applied in the present study is a cointegration-based system premised upon the RPMM.


5.2. Neuro-fuzzy system results

A step-by-step procedure is followed to construct the neuro-fuzzy system. In the first step, thefuzzy inference system is formulated in a manner that depends directly upon the cointegration results(i.e., the interactions among the variables and the sign of variables). The second step utilizes theoutput (crisp value) of the FIS as input for the FFNN.

In order to construct the FIS for the MYR/USD exchange rate, seven membership functions areintroduced. The trapezoidal membership function and triangular membership function are utilized forinputs and outputs in the FIS constructed in the present study. The structure of linguistic variablesattributed to the membership functions are ‘extremely low’, ‘very low’, ‘low’, ‘average’, ‘high’, ‘veryhigh’, and ‘extremely high’. Accordingly, seven rules are contributed to the model to generate theresults. The generated fuzzy system results become an input for the FFNN to optimize the efficiency

Table 1Cointegration tests using RPMM (Malaysia).

H0 H1 Trace Max. eigenvalue Variables Long-run coefficients

r¼0 r40 104.93n 39.63nn EXR �1.00r¼1 r41 65.29 25.98 MS 0.042r¼2 r42 39.31 20.21 Y �0.396r¼3 r43 19.09 15.46 IR 0.015r¼4 r44 3.63 2.73 INF �3.919r¼5 r45 0.89 0.89 RP �1.618

n Trace and max eigenvalue indicates one cointegrating equation at 1%.nn Trace and max eigenvalue indicates one cointegrating equation at 5%.

Table 2Cointegration tests using RPMM (Philippine).


r¼0 r40 104.65n 48.28n EXR �1.000r¼1 r41 56.37 26.25 MS �0.141r¼2 r42 30.11 19.61 Y 2.337r¼3 r43 10.50 8.32 IR 0.055r¼4 r44 2.17 2.16 INF �2.436r¼5 r45 0.00 0.00 RP �1.132

nnTrace and max eigenvalue indicates one cointegrating equation at 5%.n Trace and max eigenvalue indicates one cointegrating equation at 1%.

Table 3Cointegration tests using RPMM (Singapore).


r¼0 r40 141.72n 73.57n EXR �1.000r¼1 r41 68.14 31.76 MS �1.747r¼2 r42 36.38 16.46 Y 2.673r¼3 r43 19.92 14.11 IR �0.349r¼4 r44 5.80 5.62 INF 1.220r¼5 r45 0.18 0.18 RP �3.595

nnTrace and max eigenvalue indicates one cointegrating equation at 5%..n Trace and max eigenvalue indicates one cointegrating equation at 1%.


and accuracy of the model. Fig. 3 shows the constructed fuzzy system and the type of the membershipfunctions. The figure demonstrates that the first and the last membership functions (i.e., extremelylow and extremely high) are trapezoidal membership functions, while the remaining membershipfunctions are triangular membership functions.

In the case of PHP/USD and SGD/USD exchange rates, nine membership functions are introducedusing trapezoidal and triangular membership functions for both inputs and outputs. Consequently,nine rules are contributed to the model to generate the results. Figs. 4 and 5 show the constructedfuzzy system and the type of membership functions for the PHP/USD exchange rate and the SGD/USDexchange rate, respectively.

The fuzzy toolbox of the MATLAB program is utilized to run the FIS and generate the results. At thispoint, the results of the FIS constructed in the present study are used to develop the FFNN. Thesynthesis of FIS and FFNN is hereinafter referred as a neuro-fuzzy system. The neuro-fuzzy systemdeveloped is trained using a Levenberg–Marquardt training algorithm and predicts the exchange rate.Since the developed neuro-fuzzy system is based upon the cointegration technique, the finalconstructed model is referred to as a cointegration based neuro-fuzzy system. Figs. 6–8 show the actualreturns and generated returns of the cointegration based neuro-fuzzy system for the MYR/USD, thePHP/USD and the SGD/USD exchange rates, respectively.

As demonstrated in the figures, the cointegration-based neuro-fuzzy system is able to recognize thepattern of the return series for all exchange rates. Additionally, Table 5 shows the in-sample prediction

38 40 42 44 46 48 50 52 54 56

0

0.2

0.4

0.6

0.8

1

exr

Deg

ree

of m

embe

rshi

p

extreme low very low low average high very high very very high extreme high very very low

Fig. 4. Constructed FIS and its membership functions (PHP/USD).

3.2 3.4 3.6 3.8 4 4.2 4.4

0

0.2

0.4

0.6

0.8

1

exr

Deg

ree

of m

embe

rshi

p

extreme low very low low average high very high extreme high

Fig. 3. Constructed FIS and its membership functions (MYR/USD).

0 50 100 150-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08 MYR/USD Return SeriesReturn Generated by FIS

Fig. 6. Return series generated by constructed model (MYR/USD).

0 20 40 60 80 100 120 140 160-0.1

-0.05

0

0.05

0.1

0.15PHP/USD Return SeriesReturn Series Generated by FIS

Fig. 7. Return series generated by constructed model (PHP/USD).

1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2

0

0.2

0.4

0.6

0.8

1

exr

Deg

ree

of m

embe

rshi

p

extreme low very very low very low low average high very high very very high extreme high

Fig. 5. Constructed FIS and its membership functions (SGD/USD).


results, while Tables 6 and 7 present the out-of-sample prediction results for 3-months-ahead and 12-months-ahead, respectively.

In order to examine the prediction performance of the developed cointegration-based neuro-fuzzysystem, a vector error correction model (VECM) is adopted to determine whether the inclusion of non-linearity can improve the prediction results. To compare the forecasting performance of all models,three statistical criteria are used to compare the predicted and actual values for model validation: RootMean Square Error (RMSE), Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE).

0 20 40 60 80 100 120 140 160-0.15

-0.1

-0.05

0

0.05

0.1 SGD/USD return SeriesReturn Generated by FIS

Fig. 8. Return series generated by constructed model (SGD/USD).

Table 4diagnostic tests on VECM.

Exchange rate Applied tests Lag 3 Lag 6 Lag 12

MYR/USD Portmanteau Q-stat 103.6 210.8 430.7Prob 0.434 0.470 0.426

LM test LM-stat 44.02 27.14 70.42Prob 0.168 0.856 0.082

PHP/USD Portmanteau Q-stat 89.29 216.6 422.8Prob 0.811 0.361 0.276


SGD/USD Portmanteau Q-stat 104.4 258.8 482.4Prob 0.414 0.071 0.093



The criterion is defined, respectively, as follows:

RMSE¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi∑n

t ¼ 1ðFt�XtÞ2=n

sð5Þ

MAE¼ 1n

∑n

t ¼ 1

��Ft�Xt

�� ð6Þ

MAPE¼∑n

t ¼ 1

�� Ft �XtXt

� ��n

� 100 ð7Þ

where F is the forecasted value and X is the actual value. The RMSE and MAE criteria depend on thescale of the dependent variable. The criteria should be used as relative measures to compare forecastsfor the same series across different models. Smaller values indicate a greater forecasting performanceof the model. The MAPE criterion is scale invariant and, similar to the RMSE and MAE criteria, asmaller value indicates greater forecasting performance.

5.3. Forecasting

In order to check the goodness of fit of the VECM for prediction purposes, two diagnostic tests areemployed: the Portmanteau autocorrelation test and the LM correlation test. Table 4 shows the valuesand also the probabilities of the aforementioned tests for lags 3, 6, and 12. Both tests demonstrate theadequacy of model for prediction. The adequacy of the constructed cointegration based neuro-fuzzy

Table 5In-sample forecasting results for exchange rate' return.

Exchange rate Criteria VECM Neuro-fuzzy

MYR/USD RMSE 0.1106 0.0433MAE 0.0942 0.0235MAPE 7.36 8.0

PHP/USD RMSE 0.1540 0.1347MAE 0.1267 0.1025MAPE 3.35 29.0

SGD/USD RMSE 0.09614 0.1011MAE 0.08492 0.0758MAPE 20 15.0

Table 6Out-of-sample forecasting results for return series – 3 months ahead.


MYR/USD RMSE 0.0213 0.0406MAE 0.0208 0.0383MAPE 1.67 7.0

PHP/USD RMSE 0.01828 0.0063MAE 0.01350 0.0059MAPE 0.34 16

SGD/USD RMSE 0.01841 0.0150MAE 0.01727 0.0126MAPE 4.93 33

Table 7Out-of-sample forecasting results for return series – 12 months ahead.


MYR/USD RMSE 0.0664 0.0480MAE 0.0568 0.0394MAPE 4.56 17

PHP/USD RMSE 0.04870 0.0107MAE 0.04183 0.0085MAPE 1.08 23

SGD/USD RMSE 0.02783 0.0115MAE 0.02160 0.0090MAPE 6.26 14


system is examined for higher prediction performance, while reducing the complexity of the modelby including fewer epochs; fewer hidden layers; and fewer neurons in the hidden layers. For thispurpose, several models are developed and tested during the study. Finally, the developed neuro-fuzzysystem consists of three hidden layers with 4, 8, 4 neurons in each layer; and 200 epochs are selected.The selected model provides the most accurate prediction results, which are presented in thepresent paper.

In the case of in-sample forecasting (Table 5), the smaller value of the applied criteria generallyindicates that the cointegration-based neuro-fuzzy system outperforms the VECM model due to theadvantage of the pattern recognition in the FFNN.


Out-of-sample prediction results in Tables 6 and 7 indicate the superiority of cointegration-basedneuro-fuzzy system model over the VECM based upon the RMSE and MAE criteria. However, the short-term (3 months ahead) out-of-sample prediction results reveal that in the case of MYR, the VECMperforms better than the cointegration-based neuro-fuzzy system. However, in regards to longerhorizon prediction (12 months ahead), the cointegration-based neuro-fuzzy system outperformsthe VECM model due to the inherent advantages of a fuzzy rule based system incorporatingmacroeconomic interactions among the variables. As a result, the cointegration-based neuro-fuzzysystem is arguably a more appropriate technique for the prediction of exchange rate returns of theMYR, PHP and SGD. Interestingly, as longer horizons of prediction are considered, the performance ofintelligence systems decline (as demonstrated by the greater value of the RMSE, MAPE and MAEcriteria in longer horizons), indicating that intelligence systems are able to forecast with higheraccuracy in short-term horizons.

In order to determine whether the differences between the prediction performance criteria for thetwo models are statistically significant, the predictive accuracy of the models is further evaluatedusing the Diebold–Mariano (DM) (1995) test statistic. The null hypothesis for the test hypothesizesequal predictive accuracy between two models. Table 8 indicates that at 95% confidence interval, thenull hypothesis of no difference in the forecast accuracy of the VECM model and cointegration-basedneuro-fuzzy system is rejected. The negative value of DM test for all series, which is greater than the

Table 8Values of the Diebold–Mariano test.

Exchange rate Time period DM (VECM vs. cointegration-basedneuro-fuzzy system)

MYR/USD In-sample �4.383-months ahead �3.0612-months ahead �2.29

PHP/USD In-sample �2.183-months ahead �2.0512-months ahead �1.98

SGD/USD In-sample �3.753-months ahead �2.7112-months ahead �2.61

Table A1Unit root test for Malaysia' macro-variables.

Variables Test Level 1st difference

Intercept Trend and Intercept Intercept Trend and Intercept

Exchange rate (exr) ADF �1.21 �2.53 �16.23n �16.49n

PP �1.14 �2.62 �15.82n �16.15n

Inflation (inf) ADF �2.10 �2.23 �10.05n �10.05n

PP �1.68 �2.03 �10.02n �10.09n

National Income (y) ADF �3.27nn �2.81 �4.48n �5.12n

PP �1.47 �2.78 �32.38n �34.33n

Interest rate (ir) ADF �0.36 �1.46 �7.46n �7.65n

PP �0.31 �1.36 �6.93n �6.98n

Money supply (ms) ADF 0.62 �1.97 �9.35n �9.53n

PP 0.66 �2.27 �9.44n �9.59n

Relative price (rp) ADF �0.96 �2.77 �10.71n �10.66n

PP �1.08 �2.85 �10.67n �10.63n

nnn Denote significance at 10%.nn Denote significance at 5%.n Denote significance at 1%.


critical value of 1.96 in a normal table, indicates that the VECM model has a higher square error thanthe cointegration-based neuro-fuzzy system. The results indicate that the cointegration-based neuro-fuzzy system is a better choice than the VECM. Therefore, the results support the initial finding that thecointegration-based neuro-fuzzy system is a better model for in-sample and out-of-sample prediction.

6. Conclusion

The successful prediction of exchange rates can result in attractive benefits. As a result, suchinformation is of considerable interest for decision makers, such as financial traders, monetary policymakers and governments. The present study performs an extensive evaluation of the out-of-sampleforecasting performance of a nonlinear model-based intelligence system. We compare the predictivepower of the cointegration-based neuro-fuzzy system to the standard linear vector error correction

Table A2Unit root test for Philippine' macro-variables.

Variables Test Level 1st difference



PP �1.39 �1.12 �11.56n �11.74n


PP �0.43 �2.21 �9.49n �9.45n

National Income (y) ADF �1.79 �4.73n �4.62n �4.75n

PP �1.87 �2.09 �26.01n �28.89n

Interest Rate (ir) ADF �0.70 �1.29 �7.64n �7.69n

PP �0.80 �1.38 �6.83n �6.86n

Money Supply (ms) ADF �0.28 �4.01n �10.79n �10.77n

PP �1.95 0.26 �14.26n �14.13n

Relative Price (rp) ADF �1.12 0.29 �11.81n �10.35n

PP �1.13 0.30 �11.80n �12.33n

nnn Denote significance at 10%, nn denote significance at 5%.n Denote significance at 1%.

Table A3Unit root test for Singapore' macro-variables.

Variables Test Level 1st Difference



PP 0.15 �1.56 �12.72n �13.61n


PP �2.39 �0.67 �12.35n �12.82n

National Income (y) ADF �0.87 �4.48n �17.12n �17.08n

PP �2.34 �2.47 �44.07n �44.08n

Interest Rate (ir) ADF �1.10 �2.61 �11.16n �11.21n

PP �1.25 �2.70 �11.14n �11.18n

Money Supply (ms) ADF �0.38 �1.06 �11.07n �11.07n

PP �0.45 �1.12 �11.10n �11.09n

Relative Price (rp) ADF �2.60 �2.46 �7.10n �7.16n

PP �1.49 �1.40 �6.26n �6.27n

nnn Denote significance at 10%, nn denote significance at 5%.n Denote significance at 1%.


model for three ASEAN countries' exchange rates. To this end, we follow a step by step procedure.First, monetary fundamentals are validated through a cointegration test. Second, the interactionbetween the variables is determined based upon the values of long-run coefficients of cointegrationtests. Third, the fuzzy inference system applied in the present study is constructed based upon theinteractions determined in the second step and produces the output for the artificial neural network.Finally, the neuro-fuzzy system is formed and provides the results. Our findings show that theperformance of exchange rate prediction can be significantly enhanced by using the cointegration-based neuro-fuzzy system, which appears as a powerful tool in forecasting terms.

Acknowledgment

We would like to thank Professor Valerie Mignon, the managing editor, and two anonymousreferees for their constructive and helpful comments.

Appendix A

See Tables A1–A3.

References

Abbasi E, Abouec A., Stock price forecast by using neuro-fuzzy inference system. In: Proceedings of world academy of science,engineering and technology, vol. 36; 2008. p. 320–3.

Alakhras MNY. Neural network-based fuzzy inference system for exchange rate prediction. J Comput Sci (Special Issue) 2005:112–20.

Ang KK, Quek C. Stock trading using RSPOP: a novel rough set based neuro-fuzzy approach. IEEE Trans Neural Netw 2006;17(5):1301–15.

Armano G, Marchesi M, Murru A. A hybrid genetic-neural architecture for stock indexes forecasting. Inf Sci 2005;170:3–3.Atsalakis GS, Valavanis KP. Forecasting stock market short-term trends using a neuro-fuzzy based methodology. Expert Syst

Appl 2009b;36(3):10696–707.Balassa B. The purchasing power parity doctrine: a repraisal. J Polit Econ 1964;72(6):584–96.Boyacioglu MA, Avci D. An adaptive network-based fuzzy inference system (ANFIS) for the prediction of stock market return:

the case of the istanbul stock exchange. Expert Syst Appl 2010;37:7908–12.Brooks C. Testing for non-linearity in daily sterling exchange rates. Appl Financ Econ 1996;6:307–17.Chang PC, Liu CH, TSK A. Type fuzzy rule based system for stock price prediction. Expert Syst Appl 2008;34:135–44.Chinn MD, Before the fall: were East Asian currencies overvalued? NBER Working Paper No. 6491; 1998.Clements KW, Yihui L. A new approach to forecasting exchange rates. J Int Money and Finan 2010;29:1424–37.Diebold FX, Mariano RS. Comparing predictive accuracy. J Bus Econ Stat 1995;13(3):253–63.Dornbusch R. The theory of flexible exchange rate regimes and macroeconomic policy. Scand J Econ 1976;78(2):255–75.Egeli B, Ozturan M, Badur B., Stock market prediction using artificial neural networks. In: Proceedings of the 3rd Hawaii

international conference on business, Honolulu, Hawaii; 2003.Esfahanipour A, Aghamiri W. Adapted neuro-fuzzy inference system on indirect approach TSK fuzzy rule base for stock market

analysis. Expert Syst Appl 2010;37:4742–8.Frenkel JA. A monetary approach to the exchange rate: a doctrinal aspects and empirical evidence. Scand J Econ 1976;78(2):

200–24.Frenkel JA. On the mark: a theory of floating exchange rates based on real interest differential. Am Econ Rev 1979;69:610–22.Gradojevic N. Non-linear, hybrid exchange rate modeling and trading profitability in the foreign exchange market. J Econ Dyn

Control 2007;31:557–74.Hiemstra Y. Modeling structured nonlinear knowledge to predict stock market returns. In: Trippi RR, editor. Chaos and

nonlinear dynamics in the financial markets: theory, evidence and applications. Chicago, IL: Irwin; 1995. p. 163–75.Hopper GP, What determine the exchange rate: economic factors or market sentiment? Bus Rev; 1997; September/October:

17–29.Isard P., Factors determining exchange rates: the role of relative price levels, balance of payments, interest rates and risk, BIS

Working Paper, 4; 1980.Johansen S. Statistical analysis of cointegration vectors. J Econ Dyn Control 1988;12:231–4.Johansen S. Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models. Econometrica

1991;55:1551–80.Johansen S, Juselius K. Maximum likelihood estimation and inference on cointegration with applications to the demand for

money. Oxf Bull Econ Stat 1990;52:169–210.Kablan A. Adaptive neuro-fuzzy inference system for financial trading using intraday seasonality observation model. World

Acad Sci Eng Technol 2009;58:479–88.Karaatli M, Gungor I, Demir Y, Kalayci S. Estimating stock market movements with neural network approach. J Balikesir Univ

2005;2(1):22–48.

http://refhub.elsevier.com/S2110-7017(13)00052-8/sbref1


































Keles A, Kolcak M, Keles A. The adaptive neuro-fuzzy model for forecasting the domestic debt. Knowl-Based Syst 2008;21:951–7.

Khashei M, Bijari M. An artificial neural network (p,d,q) model for time series forecasting. Expert Syst Appl 2010;37:479–89.Khashei M, Hejazi SR, Bijari. M. A new hybrid artificial neural networks and fuzzy regression model for time series forecasting.

J Fuzzy Sets Syst 2008;159:769–86.Khashei M, Bijari M, Ardali GAR. Improvement of autoregressive integrated moving average models using fuzzy logic an

artificial neural networks. Neurocomputing 2009;72:956–67.Kia A. Determinants of the real exchange rate in a small open economy: evidence from Canada. J Int Finan Mark Inst Money

2013;23:163–78.Kodogiannis, V, Lolis, A., Prediction of foreign exchange rates by neural network and fuzzy system based techniques. ESANN

proceedings - European Symposium on Artificial Neural Networks Bruges (Belgium), 25–27 April (2001) 245–50.Leigh W, Purvis R. J.M. Ragusa, Forecasting the NYSE composite index with technical analysis, pattern recognizer, neural

network, and genetic algorithm: a case study in romantic decision support. Decis Support Syst 2002;32:361–77.Leung MT, Chen AS, Daouk H. Forecasting exchange rate using general regression neural networks. Comput Oper Res 2000;27:

1093–110.Liang YW, Tai LC, Tien HH. A hybrid model based on adaptive-network-based fuzzy inference system to forecast Taiwan stock

market. Expert Syst Appl 2011;38:13625–31.Long C, Chuen JC, Ming S. A self-organized neuro-fuzzy system for stock market dynamics modeling and forecasting. Int J Educ

Inf Technol 2010;3(4):174–86.Mamdani EH. Applications of fuzzy algorithm for control of a simple dynamic plant. Proc IEEE 1974;121(12):1585–8.Manish K, Thenmozhi M., Support vector machines approach to predict the S&P CNX NIFTY index returns. In: Proceedings of

10th indian institute of capital markets conference; 2006 Available from ⟨http://ssrn.com/abstract=962833⟩.Manzan S, Westerhoff F. Heterogeneous expectations, exchange rate dynamics and predictability. J Econ Behav Organ 2007;64:111–18.Mark NC. Exchange rates and fundamentals: evidence on long-horizon predictability. Am Econ Rev 1995;85(1):201–18.Md Nor AHS, Gharleghi B. Application of dynamic models for exchange rate prediction. Int J Innov Manag Technol 2011;2(6):

459–64.Md Nor, AHS, Gharleghi, B, Omar, K, Sarmidi, T., A novel hybrid model for exchange rate forecasting in ASEAN. In: Proceedings of

the 2nd international conference on business and economic research, Malaysia; 2011. p. 99–108.Meese RA, Rogoff K. Empirical exchange rate models of the seventies, do they fit out of sample? J Int Econ 1983a;14:3–24Meese RA, Rogoff K. The out-of-sample failure of empirical exchange rate models: Sampling error or misspecification. In:

Frankel J, editor. Exchange rates and international macroeconomics. Chicago: University of Chicago Press; 1983.Quek C. Predicting the impact of anticipator action on US stock market – an event study using ANFIS (a neural fuzzy model).

Comput Intell 2005;23:117–41.Saad EW, Prokhorov DC, Wunsch DC. Comparative study of stock trend prediction using time delay, recurrent and probabilistic

neural networks. IEEE Trans Neural Netw 1998;9:1456–70.Samuelson PA. Theoretical notes on trade problems. Rev Econ Stat 1964;46(2):145–54.Sarmidi T. Ringgit Malaysia predictability: do currencies and prediction horizon matters? J Ekon Malays 2010;44(1):51–60Satchell S, Timmermann A. An assessment of the economic value of non-linear foreign exchange rate forecast. J Forecast

1995;14:477–97.Tahmasebi P, Hezarkhani A. Application of adaptive Neuro fuzzy inference system for grade estimation; case study,

sarcheshmeh porphyry copper deposit. Aust J Basic Appl Sci 2010;4(3):408–20.Trinkle BS. Forecasting annual excess stock returns via an adaptive network-based fuzzy inference system. Intell Syst Account

Finan Manag 2006;13(3):165–77.Ucenic IC, Atsalakis G., Forecasting CPI using a neural network with fuzzy inference system. In: The XIII international conference

on applied stochastic models and data analysis, June 30–July 3. Vilnius, Lithuania; 2009.Vieira J, Dias FM, Mota A. artificial neural networks and neuro-fuzzy systems for modeling and controlling real systems: a

comparative study. Eng Appl Artif Intell 2004;17:265–73.Yu L, Shouyang W, Lai KK. A novel non-linear ensemble forecasting model incorporating GLAR and ANN for foreign exchange

rates. Comput Oper Res 2005;32:2523–41.Yudong Z, Lenan W. Stock market prediction of S&P 500 via combination of improved BCO approach and BP neural network.

Expert Syst Appl 2009;36(5):8849–54.Yunos, ZM, Shamsuddin, SM, Sallehuddin, R., Data modeling for Kuala Lumpur composite Index with ANFIS. In: Second Asia

international conference on modeling and simulation, AICMS 08, Kuala Lumpur; 2008. p. 609–14.Zadeh LA. Fuzzy sets. Inf Control 1965;8:338–53.Zhang G, Hu MY. Neural network forecasting of the British pound/US dollar exchange rate. Omega Int J Manag Sci 1998;26(4):

495–506.Zhang G, Patuwo BE, Hu MY. Forecasting with artificial neural networks, the state of the art. Int J Forecast 1998;14:35–62.



















http://ssrn.com/abstract=962833































predicting exchange rates using a novel “cointegration based neuro-fuzzy system”

Documents