Fig. 1.

This schematic illustrates the different routes one could take – using the equations in Table 1 – to derive (spectral) Granger causality measures from the (effective connectivity) parameters of a model — or indeed empirical measures of cross spectral density. The key point made by this schematic is the distinction between parametric and nonparametric spectral causality measures. These both rest upon the proportion of variance explained, implicit in the directed transfer functions; however, in the parametric form, the transfer functions are based upon an autoregression model. In contrast, the nonparametric approach uses spectral matrix factorisation, under the constraint that the spectral factors are causal or minimum phase filters. The boxes in light green indicate spectral characterisations, while the light blue boxes indicate measures in the time domain. See Table 1 and main text for a more detailed explanation of the variables and operators.