基于LSSVM的混沌时间序列的多步预测

Multi-step Prediction of Chaotic Time Series Using the Least Squares Support Vector Machines

结合相空间重构理论和统计学习理论,实现混沌时间序列的多步预测.采用微熵率法求得最优嵌入维数和时延参数,重构系统相空间,用最小二乘支持向量机建立混沌时间序列的多步预测模型,并与径向基函数网络预测模型比较.结果表明,所建立的模型能够捕捉到原混沌系统的动力学特征.前者的归一化均方根预测误差远小于径向基函数网络预测模型的预测误差,泛化能力较强,其预测效果较好.

Based on the phase space reconstruction theory and the statistical learning theory, multi-step predictions of chaotic time series are presented. The optimal embedding dimension and delay time are obtained with the differential entropy ratio method. In the reconstructed phase space, the multi-step predicting model of chaotic time series is established with the least squares support vector machines （LSSVM model） and compared with the radial basis function network predicting model （RBF model）. The results show that the proposed models can capture the dynamics of the chaotic systems. The normalized root mean square error of the LSSVM model is far less than that of the RBF model.