TABLE 5.

Frequency domain measures of causality between two processes $X_i\left(t\right)$ and $X_j\left(t\right)$ .

Direct		Strictly causal MVAR representation	Extended MVAR representation
1) Direct causality	$X_i\left(t\right)\to X_j\left(t\right)$	PDC: ${\pi }_{ij}\left(f\right)$	ePDC: ${\chi }_{ij}\left(f\right)$
2) Extended direct causality	$X_i\left(t\right)\dot{\to }{X}_j\left(t\right)$
Direct + indirect
1) Causality	$X_i\left(t\right)\Rightarrow X_j\left(t\right)$	DC: ${\gamma }_{ij}\left(f\right)$	eDC: ${\xi }_{ij}\left(f\right)$
2) Extended causality	$X_i\left(t\right)\dot{\Rightarrow }{X}_j\left(t\right)$