Noncausal Vector Autoregression

In this paper, the authors propose a new non-causal Vector Auto Regressive (VAR) model for non-Gaussian time series. The assumption of non-Gaussianity is needed for reasons of identifiability. Assuming that the error distribution belongs to a fairly general class of elliptical distributions, they develop an asymptotic theory of maximum likelihood estimation and statistical inference. They argue that allowing for non-causality is of importance in empirical economic research, which currently uses only conventional causal VAR models. Indeed, if non-causality is incorrectly ignored, the use of a causal VAR model may yield suboptimal forecasts and misleading economic interpretations.