An Approach for Short-Term Prediction on Time Series from Parameter-Varying Systems

Abstract

Time series prediction is a very important problem in many applications and the current prediction techniques are nearly all based on the Takens' embedding theorem. Many realistic systems are parameter-varying systems, and the embedding theorems are invalid, predicting the behavior of parameter-varying systems is more difficult. This paper proposes the novel prediction techniques for parameter-varying systems reconstruction, which are based on wavelet neural network (WNN) and multiwavelets neural network (MWNN). These techniques absorb the advantages of high resolution of wavelet and learning of neural networks. The significant improvement is that the error's functions of both networks are convex, and the problem of poor convergence and undesired local minimum can be solved remarkably. Ikeda time series generated by the parameter-varying systems is adopted to check the prediction performance of the proposed models. The numerical experiments show that the three proposed models are feasible, MWNN has the top performance, and WNN could lead the better results than NN in the prediction of the parameter-varying systems.