Granger causality analysis of fMRI BOLD signals is invariant to hemodynamic convolution but not downsampling.

Granger causality is a method for identifying directed functional connectivity based on time series analysis of precedence and predictability. The method has been applied widely in neuroscience, however its application to functional MRI data has been particularly controversial, largely because of the suspicion that Granger causal inferences might be easily confounded by inter-regional differences in the hemodynamic response function. Here, we show both theoretically and in a range of simulations, that Granger causal inferences are in fact robust to a wide variety of changes in hemodynamic response properties, including notably their time-to-peak.