Noncausal Vector Autoregression

In this paper, we propose a new noncausal vector autoregressive (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, we develop an asymptotic theory of maximum likelihood estimation and statistical inference. We argue that allowing for noncausality is of importance in empirical economic research, which currently uses only conventional causal VAR models. Indeed, if noncausality is incorrectly ignored, the use of a causal VAR model may yield suboptimal forecasts and misleading economic interpretations. This is emphasized in the paper by noting that noncausality is closely related to the notion of nonfundamentalness, under which structural economic shocks cannot be recovered from an estimated causal VAR model. As detecting nonfundamentalness is therefore of great importance, we propose a procedure for discriminating between causality and noncausality that can be seen as a test of nonfundamentalness. The methods are illustrated with applications to fiscal foresight and the term structure of interest rates.