Open AccessHIGHER-ORDER SINGULAR-SPECTRUM ANALYSIS OF NONLINEAR TIME SERIES
Author(s) -
Yuan Jian,
Xiao Xian-ci
Publication year - 1998
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.47.897
Subject(s) - logistic map , singular spectrum analysis , attractor , nonlinear system , mathematics , series (stratigraphy) , correlation dimension , covariance , singular value , time series , dimension (graph theory) , gaussian , lorenz system , white noise , spectrum (functional analysis) , higher order statistics , embedding , order (exchange) , covariance matrix , cumulant , computer science , algorithm , mathematical analysis , chaotic , singular value decomposition , statistics , pure mathematics , fractal dimension , physics , fractal , artificial intelligence , eigenvalues and eigenvectors , signal processing , biology , paleontology , telecommunications , quantum mechanics , radar , finance , economics
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.