Nonlinear Prediction Model Identification and Robust Prediction of Chaotic Time Series

Although, in theory, the neural network is able to fit, model and predict any continuous determinant system, there is still an obstacle to prevent the neural network from wider and more effective applications due to the lack of complete theory of model identification. This paper addresses this issue by introducing a universal method to achieve nonlinear model identification. The proposed method is based on the theory of information entropy and its development, which is called as nonlinear irreducible autocorrelation. The latter is originally defined in the paper and could determine the optimal autoregressive order of nonlinear autoregression models by investigating the irreducible auto-dependency of the investigated time series. Following the above proposal, robust prediction of chaotic time series became realizable. Our idea is perfectly supported by computer simulations.