Surrogate data approaches to assess the significance of directed coherence: application to EEG activity propagation

This paper addresses the topic of evaluating the significance of frequency domain measures of causal coupling in multivariate time series through generation of surrogate data. The considered approaches are the traditional Fourier Transform (FT) algorithm and a new causal FT (CFT) algorithm for surrogate data generation. Both algorithms preserve the FT modulus of the original series; differences are in the phase relationships, that are completely destroyed for FT surrogates and imposed after switching off the link over the considered causal direction for CFT surrogates. The ability of the algorithms to assess causality in the frequency domain was tested using the directed coherence as discriminating parameter. Evaluation on simulated multivariate linear processes and application over multichannel EEG recordings showed that the utilization of CFT surrogates improves specificity of the test for nonzero spectral causality, as FT surrogates may attribute to a direct coupling the presence of indirect connectivity patterns.