时间序列分形特征的判别

基金项目:

国家自然科学基金资助课题

详细信息

Discriminating Fractals In Time Series

摘要: 研究了判断时间序列是否具有分形特征的几个参数:庞加莱映射、李雅普诺夫指数、关联维数、功率谱及赫斯特指数,分析了它们各自的优缺点,认为:在已知动力学系统时,使用庞加莱映射和李雅普诺夫指数就能准确地判断该时间序列是否分形;在不知道动力学系统时,使用功率谱及赫斯特指数更好些,最后给出了分形在时间序列分析中适用的场合。
- 时间序列 /
- 分形 /
- 混沌
Abstract: Fractal theory is a new method to apply in time series analysis, but how to discriminate fractal time series from non-fractal time series is ambiguous. Several Parame-ters, such as Poincare map, Lyapunov exponent, correlation dimension, power spectrum density and Hunt exponent, are used to recognize if the time series are fractals. The relia-bilities of the parameters used above arc compared. If the dynamic system is known, it's fit to use the Poincare map and Lyapunov exponent; while if the dynamic system is unknown, it, s fit to use the power spectrum density and Hurst exponent. At last, the range of fractals applying in time series analysis is sketched.
- time series analysis /
- fractals /
- chaos