Gaussian小波SVM及其混沌时间序列预测

Gaussian Wavelet SVM and Its Applications to Chaotic Time Series Forecasting

为了提高混沌时间序列的预测精度,针对小波有利于信号细微特征提取的优点,结合小波技术和SVM的核函数方法,提出基于Gaussian小波SVM的混沌时间序列预测模型。证明了偶数阶Gaussian小波函数满足SVM平移不变核条件,并构建相应的Gaussian小波SVM。对混沌时间序列进行相空间重构,将重构相空间中的向量作为SVM的输入参量。用Gaussian小波SVM与常用的径向基SVM及Morlet小波SVM进行对比实验,通过对Chens混沌时间序列和负荷混沌时间序列的预测,结果表明,Gaussian小波SVM的效果比其他两种SVM更好。

To improve the accuracy of chaotic time series forecasting, Gaussian wavelet support vector machine （SVM） forecasting model is proposed, which combines the wavelet technology with SVM kernel function method, and based on that the wavelet is benefi- cial to extracting imperceptible features of signal. It is proved that the even order derivative Gaussian wavelet function is an admissible translation-invariant kernel of SVM, and corresponding Gaussian wavelet SVM is constructed. The chaotic time series is reconstructed in phase space, and the vector in phase space reconstruction is used as the input of SVM. The experiments of forecasting Chen＇s chaotic time series and load chaotic time series are conducted using the proposed SVM, the conventional radial basis SVM and the Morlet wavelet SVM respectively. The comparison results show that Gaussian wavelet SVM has better performance than the other two SVMs.