基于最小二乘支持向量回归的混沌时间序列预测研究

Research on the Prediction of the Chaotic Time Series Based on Lease Square Support Vector Machine

研究利用最小二乘支持向量机预测混沌时间序列。混沌时间序列预测是典型的小样本学习问题，基于结构风险最小化原理的支持向量机方法，克服了神经网络易于陷入局部极值点等缺点，能够获得全局最优解。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一种支持向量机，在保留支持向量机优点的同时使计算量大大减少。对典型混沌时间序列的预测结果表明，最小二乘支持向量机回归预测方法具有良好的泛化推广性能，预测精度高，适合于复杂非线性时问序列建模预测。

The chaotic time series forecast using support vector machine （SVM） was researched in this paper. The prediction of chaotic time series is belonging to the classical learning problem on small sample. The SVM method is built on the structural risk minimum theory, and overcomes the shortcoming of easily getting into the local optimization likely the artificial neural networks, so it can acquire the global optimization. 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. The forecast result on classical chaotic time series shows that the LS-SVM has the fine generalization performance and also has the higher precision, so it is fit for predicting the complex nonlinear time series.