Self-organized nonlinear prediction study for chaotic time series based on nonlinear information criterion

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The possibility of chaos presents special interest for forecasting chaotic time series data. The present paper investigates the non-linear forecasting technique in the context of deterministic chaos using both artificial and financial data. The characterization of time series by use of the delay coordinate embedding technique to construct a smooth map of the underlying dynamics becomes standard in the nonlinear time series analysis. A generalized information criterion is proposed to determine the embedding dimension and the delay time for delay coordinates of the reconstructed dynamics both for linear stochastic and nonlinear deterministic processes. While the standard maximum likelihood type method requires statistical parametric models such as autoregressive models, the generalized information criterion is constructed from the second order generalized entropy in terms of the correlation integral which is directly obtained from a time delay vector. It is found numerically that the present method works well when applied to chaotic and stochastic systems such as financial and temperature tome series.