Predict the Time Series of the Parameter-Varying Chaotic System Based on Reduced Recursive Lease Square Support Vector Machine

The forecast on the time series of the parameter -varying chaotic system using LS-SVM was researched in this paper. The SVM method is built on the structural risk minimum theory. The least square support vector machine (LS-SVM) is one kind of SVM, which solvers the problem using the equal restriction because of adopting the quadratic loss function. The LS-SVM holds the virtue of classical SVM and decrease the calculation greatly. Many chaotic system´s dynamical character always change with their parameter´s slow shifting, the global modeling forecast is not applicable, the real time online forecast method must be used. Especially such system´s time series prediction is belonging to the classical learning problem on small sample. In order to quickly track and predict these chaotic time series, on kind of reduced recursive least square support vector machine was introduced. The experiment results on the parameter-varying Ikeda equation showed that this method had better forecast performance.