a1 University of Helsinki
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 particular importance in economic applications that currently use 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. Therefore, we propose a procedure for discriminating between causality and noncausality. The methods are illustrated with an application to interest rate data.
c1 Address correspondence to Markku Lanne, Department of Political and Economic Studies, University of Helsinki, P.O. Box 17 (Arkadiankatu 7), FIN–00014 University of Helsinki, Finland; e-mail: email@example.com.
We thank Martin Ellison, Juha Kilponen, Mika Meitz, Antti Ripatti, three anonymous referees, and the co-editor, Robert Taylor, for useful comments. Financial support from the Academy of Finland and the OP-Pohjola Group Research Foundation is gratefully acknowledged. The first version of this paper was completed in May 2009. It was written while the second author worked at the Bank of Finland, whose hospitality is gratefully acknowledged.