Analysis of Vector Autoregressions in the Presence of Shifts in Mean

Abstract

This paper considers the implications of omitted mean shifts for estimation and inference in VARs. It is shown that the least squares estimates are inconsistent, and the F test for Granger causality diverges. While model selection rules have the tendency to incorrectly select a lag length that is too high, this over-parameterization can reduce size distortions in tests involving the inconsistent estimates. The practical issue of how to remove the breaks is shown to depend on whether the mean shifts are of the additive or innovational type in a multivariate setting. Under the additive outlier specification, the intercept in each equation of the VAR will be subject to multiple shifts when the break dates of the mean shifts to the univariate series do not coincide. Conversely, under the innovative outlier specification, the unconditional means of the univariate time series are subject to multiple shifts when mean shifts to the innovation processes occur at different dates: Techniques designed to detect multiple shifts are recommended when break dates do not coincide.