Feedback, causality and distance between arma models Original Research Article

The purpose of this paper is to analyze in bivariate vector autoregression the relationship between feedback in stochastic systems, Granger causality and a measure of dissimilarity between ARMA models. In particular, we consider a bivariate vector autoregressive processes of order p (a bivariate VAR(p) process) and we prove if the distance between the univariate ARMA models implied by the VAR representation is greater than a certain number that is a function of p, then Granger causality must exist in at least one direction in the variables.