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

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  • Predicting exchange rates using a novel cointegration

    Behrooz Gharleghi a,n, Abu Hasa Faculty of Business and Management, Asia Pacic U57000 Kulala Lumpur, Malaysiab Faculty of Economics and Management, Universiti K

    1. Introduction

    exchange rates are linear or non-linear remains controversial (Brooks, 1996; Satchell and Timmermann,

    Contents lists available at ScienceDirect

    International Economics

    International Economics 137 (2014) 881032110-7017/$ - see front matter & 2013 CEPII (Centre dEtudes Prospectives et dInformationsInternationales), a center for research and expertise on the world economy Published by Elsevier Ltd. All rights reserved.

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

    n Corresponding author. Tel.: +60 196153515; fax: +60 389961001.E-mail address: gharleghi.bn@gmail.com (B. Gharleghi).The foreign exchange market is the largest and most liquid of nancial markets. The issue of whetherUnit rootthree 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 dEtudes Prospectives et dInformationsInternationales), a center for research and expertise on the world

    economy Published by Elsevier Ltd. All rights reserved.a r t i c l e i n f o

    Available online 18 December 2013

    Jel classication:E47F31F37

    Keywords:Exchange rateError correction modelIntelligence systemsNeural networkssan Shaari b, Najla Shaghi b

    niversity of Technology and Innovation, TPM, Bukit Jalil,

    ebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia

    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 Articial 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 ofbased neuro-fuzzy systemjournal homepage: www.elsevier.com/locate/inteco

  • exist that may inuence 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 JohansenJuseliuscointegration technique (JJ 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 classication of soft computing techniques applied toselected ASEAN exchange rates that may be used for further analysis and evaluation; and futurecomparative studies. An obvious benet 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 prots. 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-runcoefcients. Second, once the presence of cointegrating vectors is demonstrated, the sign of coefcientsin the long-run equation is used to construct the fuzzy inference system (FIS). Finally, the generatedfuzzy inference system produces the values required for the articial 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 signicantimprovement 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 ndings 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 renetheoretical models or improve estimation techniques to explicate the puzzle (Mark, 1995; Manzan and1995; Zhang et al., 1998; Khashei et al., 2009; Zhang and Hu, 1998). However, empirical internationalnance 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 eld of economics and is widely applied in various other elds.

    Exchange rate return forecasting is a highly complicated and arduous task because many factors

    B. Gharleghi et al. / International Economics 137 (2014) 88103 89Westerhoff, 2007; Sarmidi, 2010). However, the empirical evidence consistently fails to overturn this

  • 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 signicant 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 modelidentied rules with greater interpretability and yielded signicantly higher prots 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 fuzzication 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 defuzzication 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 ll 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 inparadox. Consequently, clarifying the exchange rate predictability puzzle remains a challenging areafor contemporary researchers.

    ANNs have been successfully applied when solving problems associated with nancial time seriesforecasting, including exchange rates and nancial stock markets (Md Nor and Gharleghi, 2011;

    B. Gharleghi et al. / International Economics 137 (2014) 8810390the 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 coefcients 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 JJ 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 JJ 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:

    zt k

    i 1tzt izt1dt 1

    where zt is a vector of non-stationary variables. The matrix has reduced rank equal to r and can bedecomposed to', where and are p r full rank matrices and represent adjustment coefcients 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 JJ 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 r1 cointegrating vectors (Johansen, 1991). When the cointegrating vectors among thevariables are identied, then the sign of the coefcients 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) fuzzication, 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) defuzzication, 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 prop...

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