Multiscale Granger causality analysis by \`a trous wavelet transform

TL;DR

This paper introduces a wavelet-based multiscale Granger causality method to analyze neural interactions across different temporal scales, overcoming filtering and undersampling issues, and demonstrates its effectiveness on EEG data.

Contribution

It presents a novel wavelet transform approach for multiscale Granger causality analysis, focusing on the driver variable and using a trous wavelet with cubic B-spline filter.

Findings

Enhanced GC at slow scales during closed-eye condition

Standard GC shows no significant difference between conditions

Method effectively captures multiscale neural interactions

Abstract

Since interactions in neural systems occur across multiple temporal scales, it is likely that information flow will exhibit a multiscale structure, thus requiring a multiscale generalization of classical temporal precedence causality analysis like Granger's approach. However, the computation of multiscale measures of information dynamics is complicated by theoretical and practical issues such as filtering and undersampling: to overcome these problems, we propose a wavelet-based approach for multiscale Granger causality (GC) analysis, which is characterized by the following properties: (i) only the candidate driver variable is wavelet transformed (ii) the decomposition is performed using the \`a trous wavelet transform with cubic B-spline filter. We measure GC, at a given scale, by including the wavelet coefficients of the driver times series, at that scale, in the regression model of the target. To validate our method, we apply it to publicly available scalp EEG signals, and we find that the condition of closed eyes, at rest, is characterized by an enhanced GC among channels at slow scales w.r.t. eye open condition, whilst the standard Granger causality is not significantly different in the two conditions.