RESIDUAL ANALYSIS AND COMBINATION OF EMBEDDING THEOREM AND ARTIFICIAL INTELLIGENCE IN CHAOTIC TIME SERIES FORECASTING

Abstract

A combination of embedding theorem and artificial intelligence along with residual analysis is used to analyze and forecast chaotic time series. Based on embedding theorem, the time series is reconstructed into proper phase space points and fed into a neural network whose weights and biases are improved using genetic algorithms. As the residuals of predicted time series demonstrated chaotic behavior, they are reconstructed as a new chaotic time series. A new neural network is trained to forecast future values of residual time series. The residual analysis is repeated several times. Finally, a neural network is trained to capture the relationship among the predicted value of the original time series, residuals, and the original time series. The method is applied to two chaotic time series, Mackey-Glass and Lorenz, for validation, and it is concluded that the proposed method can forecast the chaotic time series more effectively and accurately than existing methods.