Amélioration de la prévision et causalité entre deux séries d'un systéme multivarié autorégressif stationnaire

In this paper, we study the unidirectional causal links between two series in a multivariate autoregressive stationary framework. We emphasize that the usual characterization of the unidirectional Granger causality, which is based on the prediction improvement oneperiod ahead, is not sufficient to capture all direct and indirect causal links between two series, once there exists a third serie in the system. As a consequence, following Lütkepohl [1990], we consider the prediction improvement for every prediction horizon. But contrary to this author, we do not choose to analyse the unidirectional causal links according to the Sim's approach [1980], which is based on the study of impulse coefficients. Indeed, we prove a theorem, which gives a necessary and sufficient condition to exclude any prediction improvement for every prediction horizon. According to this theorem, both characterizations of unidirectional causality appear to be complementary, because the necessary and sufficient condition is expressed as a constraint on the canonical autoregressive coefficients and the impulse coefficients respectively associated with the causal serie and the caused serie.