Model selection in partially nonstationary vector autoregressive processeswith reduced rank structure

The current practice for determining the number of linearly independent coi ntegrating vectors, or the cointegrating rank, in a vector autoregression ( VAR) requires the investigator to perform a sequence of cointegration tests . However, as was shown in Johansen (1992), this type of sequential procedu re does not lead to consistent estimation of the cointegrating rank. Moreov er, these methods take as given the correct specification of the lag order of the VAR, though in actual applications the true lag length is rarely kno wn. Simulation studies by Toda and Phillips (1994) and Chao (1995), on the other hand, have shown that test performance of these procedures can be adv ersely affected by lag misspecification. This paper addresses these issues by extending the analysis of Phillips and Ploberger (1996) on the Posterior Information Criterion (PIC) to a partial ly nonstationary vector autoregressive process with reduced rank structure. This extension allows lag length and cointegrating rank to be jointly sele cted by the criterion, and it leads to the consistent estimation of both. I n addition, we also evaluate the finite sample performance of PIC relative to existing model selection procedures, BIC and AIC, through a Monte Carlo study. Results here show PIC to perform at least as well and sometimes bett er than the other two methods in all the cases examined. (C) 1999 Elsevier Science S.A. All rights reserved.