基于支持向量机的混沌时间序列非线性预测

Chaotic Time Series Nonlinear Prediction Based on Support Vector Machines

提出一种新的应用支持向量机回归原理的混沌时间序列非线性预测方法,同时利用自适应的方法对支持向量机的参数进行优化.仿真结果显示支持向量机具有比传统的回归方法更好的泛化能力,预测方法具有很高的预测精度,同时还讨论了支持向量机中参数以及嵌入维数的变化对泛化误差的影响,得出的结论与统计学习理论中的VC维理论相一致.

Certain deterministic non-linear systems may show chaotic behavior. Time series derived from such systems seem stochastic. Sensitivity of the chaotic system to initial conditional impedes long-term predictions of time series. However, it is possible to make short-term predictions by exploiting the determinism. In this paper, a novel nonlinear prediction technique of using support vector machines （SVM） based on Statistical Learning Theory （SLT） has been proposed as well as adaptive optimization method of SVM parameters. The SVM achieves higher generalization performances than traditional regression techniques. Simulation results show the approach has better potential in the filed of chaotic time series nonlinear prediction. The effects of free parameters of SVM and embedding dimension on generalization error also have been analyzed and obtained concluaions seem consistent with the theory of VC dimension derived from SLT.