非线性时间序列的高阶奇异谱分析

基于反映线性相关结构的协方差矩阵的奇异谱分析，本质上是一种线性的方法.奇异谱分析用于吸引子重构的可靠性问题引发了一些争议.本文基于具有盲高斯噪声及体现非线性相关等性质的高阶累积量，提出了一种高阶的奇异谱分析方法.通过对Hénon映射、Logistic映射和Lorenz模型的分析说明了该方法的有效性，并在不同的延时、嵌入维数、抽样时间及有噪声的情况下表现出较好的鲁棒性. 关键词：

HIGHER-ORDER SINGULAR-SPECTRUM ANALYSIS OF NONLINEAR TIME SERIES

Singular-spectrum analysis(SSA) is essentially a linear method based on the covariance matrix which reflects the structrue of the linear dependence. Numerical experience, however,led several authors to express some doubts about reliability of SSA in the attractor reconstruction.In this paper,based on higher-order cumulants which are blind to any kind of Gaussian process and can be used for analyzing the nonlinear correlation, a new notion of higher-order singular-spectrum analysis(H-SSA) is proposed.We illustrate our technique with numerical data from Hénon map,Logistic map and Lorenz model,and show that H-SSA is robust to reconstruction delay,embedding dimension and sampling time,and to the effect of the additive noise.