A hybrid support vector regression model of chaotic time series forecasting

Traditionally, market returns have been assumed to follow the random walk hypothesis. Sakai and Tokumaru (1980) found that deterministic nonlinear equations of chaos theory could generate apparently random data. The implication is that traditional financial theory has mistaken chaos behavior for random walk. The application of chaos theory to financial theory has the potential to significantly influence the future development of the field (Peters, 1991; Papaioannou and Karytinos, 1995). In other words, traditional methodology cannot explain and predict chaos behavior. Support vectors machines (SVMs) have been successfully applied to a number of applications, including database marketing (Wright, 2003). Although SVMs have become more widely used to forecast time series data and dynamically reconstruct of chaotic systems (Drucker, Burges, Kaufman, Smola, Vapnik, 1997; Muller, Smola, Ratsch, Scholkopf, Kohlmorgen, Vapnik, 1999), it is difficult to build a highly effective model before the parameters of SVMs are carefully determined (Duan, Keerthi, and Poo, 2003). The kernel-parameters are the few tunable parameters in SVMs, controlling the complexity of the resulting hypothesis (Cristiani, Campell, and Shawe-Taylor, 1999). However, seldom articles have been devoted on the study of parameter optimization of SVMs. Hence, this study proposes a new method called genetic algorithm-support vector regression (GA-SVR) that can automatically optimize SVR parameters via the real-valued genetic algorithm with little additional computational cost and without testing on a validation dataset. Meanwhile, the proposed model can increase the accuracy of original SVM model. The GA-SVR model was tested on a forecasting a chaotic time series, weekly TWI, to show the ability of increasing accuracy.