Prediction for chaotic time series based on phase reconstruction of multivariate time series

A nonlinear prediction method based on phase reconstruction of multivariate time series was proposed. Together with the candidate time series for prediction, the correlated information of the same nonlinear dynamical system was selected to construct a multivariate time series. In the phase reconstruction space of the multivariate time series, a local multi-variant linear regression model was used to forecast the evolution data of phase point, through which the future data of the candidate time series were predicted. Since the coupled relationship among different variants of the dynamical system were taken into consideration, the reconstructed phase space had more dynamical information and phase point trajectory more approximated the original dynamical behavior. Compared with the univariate method, for either one-step or multi-step prediction, the new method has better prediction preciseness with less sensitivity to the selection of embedding dimension. The validity of the new prediction method was verified by the results of prediction experiments on the Lorenz system.