C-C method to phase space reconstruction based on multivariate time series

Based on multivariate time series phase space reconstruction theory, in this paper, we defined the nonlinear dependence measurement statistic and correlation integral for multivariate time series, and presented a C-C method for multivariate time series, which can simultaneously determine the time delay τ and embedding dimension m. The method is applied to chaotic time series, and then the obtained time delay τ and embedding dimension m are used to calculate maximum Lyapunov exponents of time series. The numerical simulations verify the effectiveness and reliability of this proposed method for choice of the time delay and embedding dimension.