title: Detection and characterization of changes of the correlation structure in multivariate time series.
abstract: We propose a method based on the equal-time correlation matrix as a sensitive detector for phase-shape correlations in multivariate data sets. The key point of the method is that changes of the degree of synchronization between time series provoke level repulsions between eigenstates at both edges of the spectrum of the correlation matrix. Consequently, detailed information about the correlation structure of the multivariate data set is imprinted into the dynamics of the eigenvalues and into the structure of the corresponding eigenvectors. The performance of the technique is demonstrated by application to N(f)-tori, autoregressive models, and coupled chaotic systems. The high sensitivity, the comparatively small computational effort, and the excellent time resolution of the method recommend it for application to the analysis of complex, spatially extended, nonstationary systems.
authors.affiliation: Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, 62210 Cuernavaca, Morelos, Mexico. muellerm@servm.fc.uaem.mx
authors.forename: Markus
authors.initials: M
authors.lastname: Müller
authors.forename: Gerold
authors.initials: G
authors.lastname: Baier
authors.forename: Andreas
authors.initials: A
authors.lastname: Galka
authors.forename: Ulrich
authors.initials: U
authors.lastname: Stephani
authors.forename: Hiltrud
authors.initials: H
authors.lastname: Muhle