Short-term prediction of chaotic time series by wavelet networks

Chaotic time series prediction is a very important problem in many applications. A number of nonlinear techniques, such as neural networks (NN), wavelets, etc., have been applied to the time series prediction problem with varying degrees of success. The novel idea in this paper is to use principal components analysis (PCA) in conjunction with a novel wavelet neural network to successfully implement the prediction of chaotic time series. It is shown that the proposed method in this paper has two-fold contributions: (1) the mean square error´s function of the network is convex and can essentially avoid the problem of poor convergence and undesired local minimum. (2) PCA can overcome the shortage that all the techniques developed for determining the embedding dimensions are inconvenient to be applied to small sample time series. The experiments also show that the proposed technique in this paper, wavelet network with PCA, is a more powerful tool for predicting chaotic series than other prediction techniques.