一种基于相空间重构的动态离散时间序列参数自适应求取算法

Adaptive calculation of dynamic discrete time series parameters based on phase-space reconstruction

提出了自适应确定动态离散时间序列的最佳重构相空间嵌入维方法,为数据量不断变动的动态离散时间序列数据库实现自动连续分析提供了可能.讨论了在应用Wolf算法计算最大Lyapunov指数时遇到的因追踪轨线追踪到相空间终点而使计算意外终止的问题,提出最大Lyapunov指数的改进求解方法.基于最大Lyapunov指数进行验证性预测,说明了算法的有效性,并进一步分析了算法对实时分析短期稳定的混沌系统具有积极意义.

This paper presents a method for calculating and automatically determining the optimal embedding dimension of the reconstructed phase-space of a dynamic discrete time series. Thus it will be possible to automatically analyze the dynamic discrete time series whose data varies continually. We discuss the problem that the calculation of the largest Lyapunov exponent, using the Wolf algorithm, may be accidentally interrupted by the trace trajectory that reaches the end of the phase-space. The presented method in this paper is confirmed feasible by using the time series proof-prediction based on the largest Lyapunov exponent. Finally, a further discussion shows that the presented method for the real-time analysis of the short-time stable Shanghai Composite Index is positive.