Testing Causality between Two Vectors in Multivariate Autoregressive Moving Average Models

Abstract

Abstract In the analysis of economic time series, a question often raised is whether a vector of variables causes another one in the sense of Granger. Most of the literature on this topic is concerned with bivariate relationships or uses finite-order autoregressive specifications. The purpose of this article is to develop a causality analysis in the sense of Granger for general vector autoregressive moving average (ARMA) models. We give a definition of Granger noncausality between vectors, which is a natural and simple extension of the notion of Granger noncausality between two variables. In our context, this definition is shown to be equivalent to a more complex definition proposed by Tjostheim. For the class of linear invertible processes, we derive a necessary and sufficient condition for noncausality between two vectors of variables when the latter do not necessarily include all the variables considered in the analysis. This result is then specialized to the class of stationary invertible ARMA process...