HYBRID SYSTEM APPLICATION FOR TIME SERIES FORECASTING: THE CASE OF MYR/USD EXCHANGE RATE

B. Gharleghi and A. H. S. Md Nor IHART - Volume 22 (2012) HYBRID SYSTEM APPLICATION FOR TIME SERIES FORECASTING: THE CASE OF MYR/USD EXCHANGE RATE Behrooz Gharleghi and Abu Hassan Shaari Md Nor University Kebangsaan Malaysia, Malaysia ABSTRACT Exchange rate prediction is a great interest and also is an important task, because, successful prediction of exchange rate may promise attractive benefits. This task is very difficult and highly complicated. In this paper, we investigate the predictability of exchange rate’ return with a Neuro-Fuzzy system (as an intelligence system) that is a combination of neural networks and fuzzy inference system. The main purpose of this research is to determine whether a Neuro-Fuzzy system is capable to predict the exchange rate’ return accurately. We attempt to model and predict the return on Malaysia Ringgit return (MYR/USD) with Neuro-Fuzzy system. The theory of relative price monetary model of exchange rate determination is used to determine the macro variables as inputs for the developed system. The experimental results reveal that the model successfully forecasts the monthly return of MYR/USD with a high accuracy. Furthermore, the constructed model easily outperformed the neural network and also random walk. The developed Neuro-Fuzzy system provides a promising alternative for exchange rate prediction. Neuro-Fuzzy system can be a useful tool for economists and practitioners dealing with the forecasting of the exchange rate return. Keywords: Exchange Rate, Forecasting, Hybrid Model, Intelligence Systems, Neural Networks. INTRODUCTION The outcomes of recent literature reveal that exchange rate return, and stock market returns are predictable from past returns and other macroeconomics variables. The predictability of exchange rate return led the researchers to investigate the sources of this predictability (Gencay, 1998). Exchange rate return forecasting is a highly complicated and very difficult task, because there exist many factors such as economic conditions, political events, traders’ expectations and other environmental factors that may influence exchange rate. Furthermore, exchange rate series are generally nonlinear, dynamic, noisy, complicated, chaotic, and nonparametric in nature (Yudong & Lenan, 2009). The techniques of soft computing are widely applied to exchange rate problems. These techniques offer useful tools to predict the date series with noisy environments such as exchange rate, and capturing their non-linear pattern (Atsalakis & Valavanis, 2009a). Application of intelligent systems such as fuzzy system and neural networks for the purpose of forecasting in the field of financial markets has extensive utilizations. For instance, artificial neural networks (ANNs) have been successfully applied to solve the problems of financial time series forecasting, including exchange rate, and financial stock market prediction (Shaari, Gharleghi 2011; Armano, Marchesi, & Murru, 2005; Egeli, Ozturan, & Badur, 2003; Hiemstra, 1995; Karaatli, Gungor, Demir, & Kalayci, 2005; Leigh, Purvis, & Ragusa, 2002; Manish & Thenmozhi, 2006; Saad, Prokhorov, & Wunsch, 1998; Yudong & Lenan, 2009, khashei, Bijari, 2010). The distinguish difference between this paper and previous research is that, (i) the constructed Neuro-Fuzzy system is not adaptive, unlike the common Adaptive Neuro Fuzzy Inference System (ANFIS) that rules are adapted. This means, in our developed system, rules are not changing during the training of the system. (ii) Multivariate neural network is constructed based on the relative price monetary model of exchange rate determination, i.e. the variables and also the interaction among the variables are extracted from the monetary model. (iii) To the best of our knowledge, very few studies have been done for the application of intelligent systems to predict the exchange rate in ASEAN-5 members, for instance ( Shaari, et. al 2011; Shaari & Gharleghi 2011) This research contributes to the field of financial market research. The main aim of this paper is to explore the predictability of exchange rate return of the Malaysian Ringgit with a Neuro-Fuzzy system. The Malaysian Exchange rate is a major economic variable that affect the other macro variables in Malaysia as a member of Association of South East Asia Nations (ASEAN). The rest of the paper is organized as follows. Section two provides a review of prior studies. Section three introduces the basic theory of Nuro-Fuzzy system. Section four describes the research findings and experimental results, while the last section discusses the conclusion and major findings of the paper. 115 Hybrid System Application for Time Series Forecasting: The Case of MYR/USD Exchange Rate LITERATURE REVIEW There has been enormous studies focus on the prediction of financial time series such as exchange rate and stock market using neuro-fuzzy systems. For instance, Kablan 2009, for the case of Euro/USD exchange rate. Abbasi and Abouec 2009 for Tehran stock exchange; Alakhras 2005, for Turkey exchange rate; Long et.al. 2010, for Taiwan stock exchange. There are a very large number of studies which concentrate on the exchange rate forecasting. In this section, we focus on the previous studies regarding the prediction of exchange rate return with neural networks and fuzzy logic. Quek (2005) applied the ANFIS to forecast the investors’ measures in the Stock Exchange Trade in United States. Model was successful to predict the stock prices in the US Stock Exchange market. Trinkle (2006) applied the ANFIS, neural network, and Autoregressive Integrating Moving Average (ARIMA) model to forecast the annual excess returns of three publicly traded companies. The forecasting performance of the two intelligent techniques is compared with ARMA model. The results reveal that the ANFIS and neural network techniques has a significant prediction ability. Yunos, Shamsuddin, and Sallehuddin (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 results show that, ANFIS is competent in forecasting the KLCI compared to artificial neural networks. Keles et al. (2008) also applied a neuro-fuzzy model to forecast domestic debt. Compared with neural network, fuzzy logic offers better insight, but its performance depends on the fuzzification of the time series data. Atsalakis and Valavanis (2009b) develop a neuro-fuzzy adaptive system to forecast the one step ahead of stock price trends for the ASE and the NYSE index. The results reveal that the proposed model performs very well in trading simulations, returning results superior to the buy and hold strategy. DATA SET AND METHODOLOGY The data used in this paper are monthly macroeconomic variables and the return of the Malaysian Ringgit over US Dollar. We obtain the monthly data set from the Thomson Data Stream data base. The whole data set covers the period from January 1998 to September 2010, a total of 153 observations for each variable. The data set is divided into two parts. The first group of the data (129 observations) is utilized for training purpose and the second group of the data (24 observations) is utilized for prediction purpose. In line with the previous literature, it is hypothesized that exchange rate return can be predicted with the financial and macroeconomic variables. According to the relative price monetary model of exchange rate determination, money supply, national income, interest rate, inflation, and customer price index as well as producer price index are the variables that determine the behavior of exchange rate (Frenkel 1976 and 1979, Dornbusch 1976, chinn 1998, Meese and Rogoff 1983), therefore, these variables used as inputs for developed neuro-fuzzy system and also neural network. In this paper, we use M2 as a representative for money supply, Industrial Production Index used as a proxy for national income due to the lack of availability of monthly data for national income. Federal fund rate is used for interest rate, other variables are used as they presented above. Output variable is the monthly return of the Malaysian Ringgit over USD exchange rate. Following the literature, we calculate the exchange rate return as follows: e  Rt  ln  t  e  t 1  (1) Where Rt denotes the return at time t, and et and et-1 are the exchange rate values for time t and t-1, respectively. THEORY OF FUZZY INFERENCE SYSTEM (FIS) A FIS can use the human expertise by storing its essentials components in a rule base, and perform fuzzy reasoning to infer the overall output value. The derivation of IF-THEN rules and corresponding membership functions depends on the a priori knowledge about the system. On the other hand, ANN learning mechanism does not rely on human expertise due to the homogenous structure of ANN, therefore it is difficult to extract the structured knowledge from either the weights or the configuration of the ANN. FIS and ANN are complementary which induce the appearance of the capacity that takes advantage of the capacity that FIS have to store human expertise knowledge and the capacity of learning of the ANN. (Vieira et.al. 2004) In this paper, all the presented results on fuzzy systems as universal approximators deal with Mamdani fuzzy system. It was proposed by Mamdani (1974) as an attempt to control a steam engine and boiler combination by synthesizing a set of linguistic 116 B. Gharleghi and A. H. S. Md Nor IHART - Volume 22 (2012) control rules obtained from experienced human operators. Mamdani’s efforts were based on Zadeh’s (1965) paper on fuzzy algorithms for complex systems and decision processes. Mamdani type inference system suggests that the output membership functions to be fuzzy sets. The working of FIS can be explained as below. The crisp input is transformed in to fuzzy by the fuzzification method. After fuzzification the rule base is made. The rule base and the database are together referred to as the knowledge base. Defuzzification is used to transform fuzzy value to the real world value which is actually the output. (Figure 1) Knowledge Base Input Database Output Rule Base Fuzzification Inference Defuzzification Inference (Crisp) (Crisp) Decision Making Unit (Fuzzy) (Fuzzy) Figure 1: Fuzzy Inference System Fuzzification is the method where the crisp quantities are transformed to fuzzy sets. By identifying some of the uncertainties present in the crisp values, we formulate the fuzzy values. The transformation of fuzzy values is represented by the membership functions. It classifies the element in the set, for both discrete and continuous. The “shape” of the membership function is an important criterion that is to be considered. The rule-based fuzzy system form uses linguistic variables as its antecedents and consequents. The fuzzy rule-based system uses IF–THEN rule-based system, given by, IF antecedent, THEN consequent. The conversion of fuzzy to crisp values is defuzzification. The fuzzy results obtained cannot be used as such to the applications, and thus it is necessary to transform the fuzzy quantities into crisp quantities for further processing. This can be done by using defuzzification process. The decision-making is a major part in the entire system. The FIS forms suitable rules and based upon those rules the decision is made. This is based on the concepts of the fuzzy set theory, fuzzy IF–THEN rules, and fuzzy reasoning. FIS uses “IF. . . THEN. . . ” statements, and the connectors used in the rule statement are “OR” or “AND” to formulate the necessary decision rules. ARTIFICIAL NEURAL NETWORKS Neural Network is a modeling method based on the human brain that can recognize and learn the pattern of the foreign exchange rate through past data, save these rules and forecast the future exchange rate. For ANN, there is no need to specify any particular model, because, ANN can be adapted based on the features presented in the data set. The great advantage of neural networks is their flexible ability to model the nonlinear patterns and it is adapted based on the features of the data set that can be called as a data driven approach. This approach is useful for many empirical researches in which there is no theoretical guideline available to suggest an appropriate data generating process. (Shaari, Gharleghi 2011) ANNs are the appropriate methods to forecast the exchange rate due to some unique features. First, ANNs are self adaptive in that there are few assumptions about the models, so neural networks are less impressible in model misspecification problem. Second, Generalization ability, after learning the pattern of data set given to them, ANNs can infer the unseen part of population, even if data set contain noisy information. Third, ANNs are Non linear, based on time series prediction models like ARIMA, always assumed that the time series generated from a linear process. Fourth, ANNs are universal functional estimators; it means a network can estimate any continuous function to any desired accuracy. (khashei , bijari 2010) Feed Forward Neural Network is the most widely used network in which all layers except input layer receive weights from their previous layer. This network is consisted of three layers; input layer which includes explanatory variables (inputs) in the model. Hidden layer; lies between the input and output layers. There can be many hidden layers, which allow the network to learn, adjust, and generalize from the previously learned facts (data sets) to the new input. The number of hidden layers and nodes in the network are determined by trial and error, and this paper follows this technique. Output layer is including the output of network. 117 Hybrid System Application for Time Series Forecasting: The Case of MYR/USD Exchange Rate Single hidden layer feed forward network is represented as follow for time series modeling and forecasting, it has three layers of simple processing units connected by acyclic links: yt  w0   w j .g ( w0, j   wi , j . yt i )   t q p j 1 j 1 (2) where, wij (i = 0,1,2,…,p, j=1,2,…,q) and wj (j=0,1,2,…,q) are model parameters called connection weights; p is the number of input nodes; and q is the number of hidden nodes. Figure 2 represents the simple structure of feed forward neural network: Figure 2: Structure of Three Layers Neural Network Neurons must use activation function to generate the output. Activation function represents a degree of nonlinearity which is valuable for neural networks applications. Activation function can take several forms; the type of this function is specified by the situation of the neuron within the network. The sigmoid, tangent hyperbolic, and a combination of both are the activation functions (tansig) which mostly used as the hidden layer transfer function. In this paper the “tansig” activation function is used and can be represented in following equation: tan sig ( x )  2 1 (1  e 2n ) (3) RESEARCH RESULTS In this paper, a stepwise procedure is followed to construct the neuro-fuzzy system; first, we attempt to form the fuzzy inference system, and second, is to use the output (crisp value) of the fuzzy inference system as an input to the neural network. In order to build up the fuzzy inference system, seven membership functions are introduced and the types of the membership functions are the combination of trapezoidal and triangular for each input as well as output. Accordingly seven rules have been contributed to the model to generate the result. The generated fuzzy system result, hence, becomes an input for the artificial neural network to optimize the efficiency and accuracy of the model. Figure 3 shows an example of the type of the membership function. From the figure, it can be seen that the first and the last membership functions are trapezoidal and the rest are triangular type. 118 B. Gharleghi and A. H. S. Md Nor IHART - Volume 22 (2012) extreme low very low 1 low average high very high extreme high Degree of membership 0.8 0.6 0.4 0.2 0 3.2 3.4 3.6 3.8 exr 4 4.2 4.4 Figure 3: Structure of the Membership Functions In order to compare the performance of neuro-fuzzy system, a multivariate neural network is also introduced and include three layer, one input layer with five neurons that represent the inputs, one hidden layer, and one output layer that represent the return of exchange rate. In input layer, there are money supply, industrial production index, interest rates, inflation, consumer price index, and producer price index. The return of the Malaysian Ringgit exchange rate is in the output layer. To compare the forecasting performance of developed models, some statistical methods, such as the root mean squared error (RMSE), the mean absolute error (MAE), the mean absolute percentage error (MAPE), and variance proportion (VP) are used to compare the predicted and actual values for model validation. The RMSE and MAE can be defined as: RMSE  MAE   (F  X ) n t 1 t t 2 /n (4) 1 n  Ft  X t n t 1 (5) where F is the forecasted value and X is the actual value. RMSE and MAE criteria depend on the scale of the dependent variable. These should be used as relative measures to compare forecasts for the same series across different models; the smaller value means the better the forecasting of that model. In addition, the mean absolute percentage error and variance proportion can be written as:  n MAPE  V .P  t 1 Ft  X t Xt n  100 (6) (s yˆ  s y ) 2  (F  X ) (7) n t 1 t t 2 /n where, sŷ is the standard deviation of forecasted series and sy is the standard deviation of actual series. MAPE is scale invariant and the better the forecasting performance results from smaller value of MAPE. The variance proportion tells us how far the variation of the forecast is from the variation of the actual series. 119 Hybrid System Application for Time Series Forecasting: The Case of MYR/USD Exchange Rate The computer program was performed on MATLAB (version 9, The MathWorks Inc., USA) environment by using the fuzzy toolbox. The developed Neuro-Fuzzy topologies with seven input membership functions were trained. Figure 4 shows actual return and generated return by Fuzzy inference system. 0.08 MYR/USD Return Series Return Generated by FIS 0.06 0.04 0.02 0 -0.02 -0.04 -0.06 0 50 100 150 Figure 4: Factual and Forecasted return Series via Fuzzy Inference System As figure above shows, the neuro-fuzzy system was able to recognize the pattern of the actual return series for MYR/USD exchange rate. However, the prediction results are presented in table 1, and 2 for in sample forecasting and out of sample forecasting respectively. As it can be observed from the table, random walk results also presented to ensure that the developed models are adequate. In the case of in-sample forecasting, in general, intelligent systems easily outperform the random walk model as indicated by smaller value of mentioned criteria. More specific, the prediction performance of neural network is better than the developed neuro-fuzzy system that is due to the advantage of pattern recognition by multivariate neural networks. Table 1: In Sample Forecasting Results for Return Series (MYR/USD) Model RW(with drift) Neural Network Neuro-Fuzzy RMSE 0.3313 0.00308 0.0433 MAE 0.2653 0.00107 0.0235 MAPE 6.8 1.1 8 VP 0.1949 0.00131 0.00324 However, the out of sample forecasting results are provided for short, and medium term and reveals that, Intelligent systems outperformed the random walk model in all time horizon forecasting. As it is clear for out of sample prediction, the ability of neuro-fuzzy system is obvious to outperform the neural network. This is due to the advantage of fuzzy rule based system that incorporates the macroeconomic relationships among the variables. As a result, it can be said that the developed neuro-fuzzy system is an appropriate technique for the prediction of exchange rate return. Interestingly, as the longer horizon is considered, the performance of intelligent systems declines (it can be seen as the greater value of criteria in longer horizon), means, intelligence system are able to forecast with higher accuracy in short-term forecasting. But random walk provides a mixed result. 120 B. Gharleghi and A. H. S. Md Nor IHART - Volume 22 (2012) Table 2: Out of Sample Forecasting Results for Return Series (MYR/USD) Model RW (with drift) Neural Network Neuro-Fuszzy 3 Steps Ahead RMSE 0.0955 0.0403 0.0357 MAE 0.0857 0.0397 0.0323 MAPE 2.3 7.5 7 VP 0.3126 0.00682 0.00419 6 Steps Ahead RMSE 0.1172 0.0492 0.0399 MAE 0.1087 0.0449 0.0374 MAPE 3 8.5 14 VP 0.1991 0.00795 0.00368 12 Steps Ahead RMSE 0.0919 0.07390 0.0514 MAE 0.0790 0.07154 0.0416 MAPE 2.2 5.9765 8 VP 0.1257 0.0399 0.0278 CONCLUSION Predicting the exchange rate return is important and is a great interest, because, successful prediction of exchange rate may promise attractive benefits. It usually affects the financial trader’s decision, monetary policy makers, and government policy to import or export the commodities. Soft computing techniques have been successfully applied to provide a high accuracy result for exchange rate prediction. In this paper, the neuro-fuzzy system is adopted to predict the exchange rate return on the Malaysian Ringgit. The result of the study shows that the performance of exchange rate prediction can be significantly enhanced by using Neuro-fuzzy system. Based on the experimental results, the value of the comparison criteria is obtained and they are very satisfying. The prediction performance of this method shows the advantages of Neuro-fuzzy system. The findings demonstrate the learning and predicting potential of the Neuro-fuzzy system in financial applications. Furthermore, these results indicate that neuro-fuzzy system can be a useful tool for the prediction of MYR/USD exchange rate. REFERENCES Abbasi, E., & Abouec, A. 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