CHAOTIC TIME SERIES ANALYSIS AND PHASE SPACE RECONSTRUCTION BASED ON WAVELET NEURAL NETWORKS

In this paper, the applications of a kind of wavelet neural networks （WNNs） in chaotic time series analysis and phase space reconstruction are investigated. The approximation and convergence performance of WNNs and mulitlayer perceptions（MLPs） are compared in the applications of single and multiple step prediction of chaotic time series. Besides, an improved multiresolution learning paradigm is proposed, in which the original Haar wavelet is substituted by the cubic spline wavelet and Daubechies orthogonal wavelet in the wavelet decomposition. The improved learning algorithm is utilized to process the original data for training WNNs and applied in the phase reconstruction of chaotic time series. The experimental results demonstrate that WNNs have greater approximation ability than MLPs as well as ARMA models, hence the WNN model seems more suitable in time series analysis; and the multiresolution learning algorithm is a powerful tool for analyzing the complex chaotic time series.