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 Henon 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.