Support Vector Regression with Kernel Mahalanobis Measure for Financial Forecast

Abstract

For time series forecasting which have data sets coming from an unstable and nonlinear system such as the stock market. Support Vector Regression (SVR) appears to be an efficient tool which has been widely used in recent years. It is also reported to have a higher accuracy and generalization ability than other traditional methods. The SVR method deals with the nonlinear problem by mapping the input feature space into a high dimensional space so that it becomes a linear problem. Kernel function is one of the crucial components in SVR algorithm as it is used to calculate the inner product between vectors in the mapped high dimensional space. The kernel function of Radial Basis Function (RBF), which is based on the Euclidean distance, is the most commonly used kernel function in SVR. However, the SVR algorithm may neglect the effect of correlation among the features when processing the training data in time series forecasting problems due to the limitation of Euclidean distance. In this chapter, a Mabalanobis distance RBF kernel is introduced. It is well known that when we need to calculate similarity between two vectors (samples), the use of Mahalanobis distance can take into account the correlation among the features. Thus, the SVR with Mahalanobis distance kernel function may follow the behavior of the data sets better so that it can give more accurate result. From the comparative investigation, we find that in some circumstances, the Mabalanobis distance RBF kernel based SVR can outperform the Euclidean distance based SVR.