Fully Modified VAR Inference in Partially Nonstationary Models
Simon School, University of Rochester
To test for the number of cointegrating relationships among multivariate time series, the likelihood ratio (LR) test for ranks is commonly used. The distribution of the LR test in partially nonstationary models is nonstandard and nonsymmetric in the presence of non-iid errors. In contrast we show that, under less restrictive assumptions on the errors, the fully modified (FM), VAR rank test has a x2 distribution for the null of cointegration but is degenerate for the null of no cointegration, unlike its LR counterpart which is well defined for both nulls. It turns out that augmenting the VAR by an exogenous I (0) variable solves the degeneracy problem. The procedure can also be applied to testing for Granger-Causality and is, in fact, a generalization of Toda-Yamamoto=D5s (1995) procedure of augmenting the VAR with additional lagged I (1) variables. Unlike Toda-Yamamoto=D5s approach, our FM tests do not require knowledge of the number of lagged variables in the VAR nor does it require errors to be iid.
JEL Classification: C12, C32
Date posted: July 1, 1997