SupportVector Fuzzy BasedNeuralNetworks For Exchange RateModeling

In modeling some systems where available information is uncertain, we must deal with a fuzzy structure of the system considered. This structure is represented as a fuzzy function whoseparameters are given by fuzzy sets. The fuzzy functions are defined by Zadeh’s extension principle [1], [2], [3]. The Support Vector Machines (SVMs), developed at AT&T Bell Laboratories by Vapnik and co-works [4], [5], have been very successful in pattern classification and function estimation problems for crisp data. It is based on the idea of structural risk minimization, which shows that the generalization error is bounded by the sum of thetraining error and a term depending on theVapnik–Chervonenkis (VC) dimension. By minimizing this bound, high generalization performance can be achieved. A comprehensive tutorial on SVM classifier has been published by Burges [6]. In regression and time series prediction applications, excellent performances were also obtained in. Lin et al. [7] and Huang et al. [8] first introduced the use of fuzzy set theory for SVM classification problems. Using hybrid models or combining several models has become a common practice to improve forecasting accuracy.The li terature on this topic has expanded dramatically since the early work of Reid [9]. The basic idea of the model combination in forecasting is to use each model’s unique feature to capture different patterns in the data. Both theoretical and empirical findings suggest that combining different methods can be an effective and efficient way to improve forecasts [11]. Slim [11] and [12] proposed an hybrid approach based on neural network and fuzzy system for financial time series forecasting and bankruptcy prediction to use the advantages and to fulfill the limitations of the two systems. In this paper, we incorporated the concept of fuzzy set theory into the SVM regression and Neural ntworks modeling. A novel fuzzy neural network combining with support vector learning mechanism called support-vector-based fuzzy neural networks (SVBFNN) is proposed. The SVBFNN combine the capability of minimizing the empirical risk (training error) and expected risk (testing error) of support vector learning in high dimensional dataspacesand theefficient human-like reasoning of FNN. A learning algorithm consisting of three learning phases is developed to construct theSVBFNN and train the parameters. In the first phase, the fuzzy rules and membership functions are automatically determined by the clustering principle. In the second phase, the parameters of FNN are calculated by the SVR with the proposed adaptive fuzzy kernel function for time series prediction. In the third phase, the relevant fuzzy rulesareselected by theproposed fuzzy rulereduction method. The paper is organized as follows: the structure and the learning algorithme behavior of the proposed SVBFNN are described in Section 2. The proposed model is used to predict currency exchange rate between EURO/TND, USD/TND, GBP/TND and JPY/TND. and is compared with some parametric models such as ARIMA, VAR and nonparametric techniques such as SVR and BNN in Section 3. Conclusion is summarized in the last section.