Generating surrogate data for time series with several simultaneously measured variables

TL;DR

This paper introduces an extended phase-randomized Fourier-transform method to generate surrogate multivariate time series data that preserve both autocorrelations and cross-correlations, validated on simulated and EEG data.

Contribution

It presents a novel extension of the Fourier-transform surrogate method to multivariate data, capturing both autocorrelations and cross-correlations.

Findings

Successfully applied to Lorenz system data

Effectively mimics EEG multichannel data

Preserves autocorrelation and cross-correlation structures

Abstract

We propose an extension to multivariate time series of the phase-randomized Fourier-transform algorithm for generating surrogate data. Such surrogate data sets must mimic not only the autocorrelations of each of the variables in the original data set, they must mimic the cross-correlations {\em between} all the variables as well. The method is applied both to a simulated example (the three components of the Lorenz equations) and to data from a multichannel electroencephalogram.