Granger causality in a bivariate frame

The present article enounces two theorems which establish the equivalent conditions that have to be satisfied in the different ways in which the lineal bivariate models of time series may be expressed in order to characterize the two basic events of (non) causality enounced with Granger’s definition as a starting point: (non) unidirectional causality and (non) instantaneous causality. The theorems in question are a revision of those stated by Pierce and Haugh. Thus, on the one hand they modify some of the conditions enounced by said authors and on the other hand they consider conditions they have not taken into account. Moreover, an analysis is also made of how these theorems may be influenced as a consequence of identifying the model through the imposition of other parametric restrictions which differ from those studied by Pierce and Haugh.