Prediction of Chaotic Time Series Based on Kernel Function and Multi-scales Wavelet Transform

According to the noise in the nonlinear systems and shortage of chaotic prediction method at present, this paper presents a local linear adaptive prediction algorithm based on the kernel function of wavelet decomposition. This method using wavelet transformation has a unique multi-scale analysis capability, decomposed the singular into low frequency part and high frequency part, thereby it can reduce the degree of nonlinear time series and make the issue easy to analyze and predict. Analysis of each part indicates that there exists a chaos feature. Then novel local linear predicting models based on kernel function are established, this model is equivalent to estimate high-complicated nonlinear chaotic series by high-complicated nonlinear function in the origin phase space, and can predict chaotic sequence more exactly.  At last, forecasting results of the chaotic models are reconstructed which is based on wavelet theory, so as to forecast the system feature reference data series. The following simulation results show the effectiveness of the method described.