Abstract: The forecast on the time series of the parameter-varying chaotic system using LS-SVM is researched in this paper.The SVM method is built on the structural risk minimum theory.The least square support vector machine（LS-SVM） is a 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 trace and predict these chaotic time series，a kind of reduced recursive lease square support vector machine is introduced.The experiment results on the parameter-varying Henon map and Ikeda equation show that this method has better forecast performance.

Key words: chaos, time series, predict, Least Square Support Vector Machine（LS-SVM）

摘要： 研究利用最小二乘支持向量机（LS-SVM）预测变参数混沌时间序列。支持向量机方法是基于结构风险最小化原理导出的，最小二乘支持向量机是一种在二次损失函数下采用等式约束求解问题的支持向量机，保留支持向量机优点的同时计算量大大减少。变参数混沌时间序列预测是典型的小样本学习问题，由于参数的慢变导致系统的动力学特性不断发生变化，全局建模预测方法很难适用，必须在线实时预测。为了快速跟踪预测变参数混沌系统的时间序列，研究了利用一种简化的最小二乘支持向量机在线递推算法进行预测。最后对典型变参数混沌时间序列的预测实验结果表明了该方法的有效性。

关键词: 混沌, 时间序列, 预测, 最小二乘支持向量机