Accuracy in forecasting business cycles is an important issue in economic study, and statistical methods have usually been employed to analyze them. Many investigations have been done in the analysis of business cycles (Banerji and Hiris, 2001, Layton, 1996, Layton, 1998, Seip and McNown, 2007, Wu and Tseng, 2002 and Yang and Kim, 2005). However, business cycles are often determined by a panel of macroeconomic experts, and thus, it is difficult to predict the index of business cycles. The difficulty arises from assumptions made from the probability distributions and business cycle data, which are usually vague. The index of business cycles in Taiwan is composed of nine exogenous variables, and five lights are used to represent different economic activities. The five lights include some uncertain factors in predicting business cycles. Hence, the fuzzy set theory (Zadeh, 1965) is a proper approach to analyze Taiwan business cycles.
Unlike most of traditional technologies SVR (Vapnik, Golowich, & Smola, 1996) implementing neural network models, SVR adopts a structural risk minimization principle, which seeks to minimize the upper bounds of the generalization error rather than minimize the training error. In recent years, SVR schemes have been extended to cope with forecasting problems, and have provided many promising results in customer demand (Levis & Papageorgiou, 2005), finance (Huang et al., 2005, Kim, 2003 and Tay and Cao, 2002), intermittent demand (Hua & Zhang, 2006), tourism demand (Pai & Hong, 2005), air quality (Lu & Wang, 2005), wind speed (Mohandes, Halawani, Rehman, & Hussain, 2004), plant control systems (Xi, Poo, & Chou, 2007), rainfall (Hong & Pai, 2007), prices for the electricity market (Gaoa, Bompard, Napoli, & Cheng, 2007), and flood control (Yu, Chen, & Chang, 2006). Hong and Hwang (2003) proposed a support vector fuzzy regression machine model for modifying convex optimization problems of multivariate fuzzy linear regression models. Empirical results indicate that the developed model derives satisfying solutions efficiently. Jeng, Chuang, and Su (2003) developed a support vector interval regression network to efficiently handle interval output data. Yao and Yu (2006) developed a fuzzy regression based on asymmetric support vector machines, which overcome limitations of traditional nonlinear fuzzy regression, and can be effectively used for parameter estimation. Chuang (2008) presented an interval support vector regression network model, which can handle interval input and output data. Hao and Chiang (2008) developed a fuzzy regression analysis model based on support vector learning techniques, and suggested that the developed model can perform automatic and accurate control in fuzzy regression analysis tasks.
In this study, a fuzzy support vector regression model is presented to forecast an index of business cycles. Support vector regression was used to calculate fuzzy upper and lower bounds, and then make predictions by fuzzy H-level set (H-cut). In addition, genetic algorithms (GA) were employed to select three parameters of SVR models. The remainder of this paper is organized as follows. A brief introduction of the theory of SVR is given in Section 2. The fuzzy support vector regression model is derived in Section 3. A numerical example of business cycle predictions and empirical results are presented in Section 4. Some concluding remarks are offered in Section 5.
Due to the recent global economic recession, analysis of business cycles is increasingly crucial. This study develops a FSVR model to exploit the unique strength of the fuzzy set theory and the SVR technique, in order to predict business cycles in Taiwan. Simulation results indicate that the FSVR model offers a promising alternative in business cycles in uncertain circumstances. The superior performance of the FSVR model can be ascribed to two causes. First, the SVR can efficiently capture trends of nonlinear data, and precisely estimate upper bounds and lower bounds of fuzzy numbers. Second, based on sensitive analysis of H-level, the FSVR model can provide creditable predictions for Taiwanese business cycle predictions. For future work, forecasting other types of uncertain time series data by the FSVR model is a challenging issue for study. Future studies can also consider using data preprocessing techniques to improve the forecasting accuracy of the FSVR model.
