Multiscale Granger causality analysis by a trous wavelet transform

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 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 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 the causality, 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 public scalp EEG signals, and we find that the condition of closed eyes, at rest, is characterized by an enhanced Granger causality among channels at slow scales w.r.t. eye open condition, whilst the standard Granger causality is not significantly different in the two conditions.