Lag length and mean break in stationary VAR models

We consider three approaches to determine the lag length of a stationary vector autoregression model and the presence of a mean break. The first approach, commonly used in practice, uses a break test as a specification check after the lag length is selected by an information criterion. The second performs the break test prior to estimating the lag length. The third simultaneously selects both the lag length and the break by some information criterion. While the latter two approaches are consistent for the true lag order, we justify the validity of the first approach by showing that the lag length estimator based on specific information criteria is at worst biased upwards asymptotically when the mean break is ignored. Thus, conditional on the estimated lag length, the break test retains its asymptotic power properties. Finite-sample simulation results show that the second approach tends to have the most stable performance. The results also indicate that the best strategy for short-run forecasting does not necessarily coincide with the best strategy for finding the correct model. Copyright Royal Economic Society, 2002