Rapid surrogate testing of wavelet coherences

Lawrence W Sheppard,Daniel C Reuman,Philip C Reid

doi:10.1051/epjnbp/2017000

Abstract

Background. The use of wavelet coherence methods enables the identification of frequency-dependent relationships between the phases of the fluctuations found in complex systems such as medical and other biological timeseries. These relationships may illuminate the causal mechanisms that relate the variables under investigation. However, computationally intensive statistical testing is required to ensure that apparent phase relationships are statistically significant, taking into account the tendency for spurious phase relationships to manifest in short stretches of data.

Highlights

In biophysical systems, multivariate data is often autocorrelated and cross correlated and incorporates a spectrum of fluctuations on different timescales
Coherence values not significant at the p < 0.05 level are masked with green, whereas significant values are indicated by a filled square with a colour indicating the phase shift between the variable indicated on the y axis and that on the x axis
Wavelet coherence or spatial wavelet coherence of real or surrogate data can be rapidly calculated via our new method

Summary

Introduction

Multivariate data is often autocorrelated and cross correlated and incorporates a spectrum of fluctuations on different timescales. The use of wavelet coherence methods enables the identification of frequencydependent relationships between the phases of the fluctuations found in complex systems such as medical and other biological timeseries These relationships may illuminate the causal mechanisms that relate the variables under investigation. In this study we revisit Fourier transform based methods for generating surrogate data, with which we sample the distribution of coherence values associated with the null hypothesis that no actual phase relationship between the variables exists. The properties of this distribution depend on the cross-spectrum of the data. Our new technique enables enormously faster significance testing of wavelet coherence

Methods

Results

Conclusion