Phase space reconstruction and prediction of multivariate chaotic time series

In order to obtain the effective input vector for the prediction of multivariate time series, method of joint entropy determine the dimension(JEDD) is proposed in the reconstructed phase space. For multivariate chaotic time series, Firstly, determine the delay time of each variate with mutual information method, and then propose the algorithm that determines the embedding dimension of phase space by the joint entropy. The algorithm could choose the reconstructed components based on the maximum entropy principle, continuously expand phase space to make the amount of the information of reconstructed components as much as the system, which could eliminate the redundancy of phase space. The numerical experiments show that the neutral network prediction in the reconstructed phase space by JEDD is much better than univariate time series prediction and existing multiple variable predictions.