The Wavelet Transform with best decomposition Level and Relevant Vector Machine Based Approach for Chaotic Time Series Forecasting

In order to accurately predict the chaotic time series, a novel approach based on integration of wavelet transform and Relevant Vector Machine (RVM) is proposed. The best wavelet decomposition level is determined with the condition that a certain function space orthogonal projection energy in wavelet MRA, is smaller than the largest energy of the forecasting biases. Delay mapping is introduced to transform the different components into new samples of historical characteristics, after wavelet transform. The different new samples are predicted by their corresponding forecasters, respectively. The final forecasting result is obtained by combining all the predicted results. The sparse relevant support vector and its corresponding hyper parameters are calculated on the new sample space of time series by the Sparse Bayesian learning process. Based on which the prediction results are work out. The results show that the approach only using the SVM or RVM based forecaster the averaged prediction biases is more than 10%. The tracking ability and the dynamic behavior are remarkably improved to the averaged biases of 5.43% by using the wavelet transform with best decomposition Series and RVM based forecaster. It is indicated that the suggested approach is feasible and effective.