Estimating the strength of genuine and random correlations in non-stationary multivariate time series

¹  Facultad de Ciencias, Universidad Autónoma del Estado de Morelos - 62209 Cuernavaca, México
²  Max-Planck-Institut für Physik komplexer Systeme - D-01187 Dresden, Germany, EU
³  Manchester Interdisciplinary Biocentre, University of Manchester - Manchester M1 7DN, UK, EU
⁴  Department of Neurology, Inselspital, Bern University Hospital, and University of Bern - Switzerland

Corresponding author: muellerm@buzon.uaem.mx

Received: 4 June 2008
Accepted: 25 August 2008

Abstract

The estimation of the amount of genuine cross-correlation strength from multivariate data sets is a nontrivial task, especially when the power spectra of the signals vary dynamically. In this case, the amount of random correlations may vary drastically, even when the length T of the data window used for the construction of the zero-lag correlation matrix is kept constant. In the present letter we introduce correlation measures that allow to distinguish quantitatively genuine and random cross-correlations. The measures are carefully tested by employing model data and exemplarily we demonstrate their performance by their application to a clinical electroencephalogram (EEG) of an epilepsy patient.