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

混沌的可能性对混沌时间序列数据的预测具有特殊的意义。本文利用人工数据和金融数据研究了确定性混沌环境下的非线性预测技术。在非线性时间序列分析中，利用延迟坐标嵌入技术构造底层动力学的平滑映射来表征时间序列已成为标准方法。针对线性随机过程和非线性确定性过程，提出了一种广义信息准则来确定重构动力学的嵌入维数和延迟坐标的延迟时间。标准的极大似然型方法需要自回归模型等统计参数模型，而广义信息准则是由二阶广义熵根据直接从时滞向量中得到的相关积分来构造的。数值结果表明，该方法适用于金融和温度序列等混沌和随机系统。

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.