Chaotic Time series Prediction using Wavelet Neural Network

Abstract

Time series prediction from a given set of input/output data (I/O) is an important problem in many real applications. This problem consists of the prediction of future values based on past and/or present data. A number of nonlinear techniques, such as RBF neural networks (RBFNs), Wavelet Neural Networks (WNNs), etc., have been applied to the time series prediction problem. In this paper, we present a new approach for prediction of time series data using WNNs. This approach based on a new efficient approach of optimizing the position of the mother wavelet of the WNN; it uses the real output of WNN to move the position of wavelet single function. This method divides the input data space in parts, depending on each mother wavelet and which data belongs to it, then calculates the error committed in every mother wavelet area trying to concentrate more mother wavelets (neurones) in those input regions where the error is bigger, thus attempting to homogenize the contribution to the error of every mother wavelet. The paper presents two examples of Wavelet Neural Networks applied on Mackey-Glass time series data prediction in Short-term prediction and Large-term prediction. This approach improves the performance of the prediction system obtained, compared with other approaches that use RBFNN derived from traditional algorithms.