A Comparison of Sequential and Information-based Methods for Determining the Co-integration Rank in Heteroskedastic VAR Models

Abstract

In this paper we investigate the behaviour of a number of methods for estimating the co-integration rank in VAR systems characterized by heteroskedastic innovation processes. In particular we compare the efficacy of the most widely used information criteria, such as AIC and BIC, with the commonly used sequential approach of Johansen (1996) based around the use of either asymptotic or wild bootstrap-based likelihood ratio type tests. Complementing recent work done for the latter in Cavaliere, Rahbek and Taylor (2013, Econometric Reviews, forthcoming), we establish the asymptotic properties of the procedures based on information criteria in the presence of heteroskedasticity (conditional or unconditional) of a quite general and unknown form. The relative finite-sample properties of the different methods are investigated by means of a Monte Carlo simulation study. For the simulation DGPs considered in the analysis, we find that the BIC-based procedure and the bootstrap sequential test procedure deliver the best overall performance in terms of their frequency of selecting the correct co-integration rank across different values of the co-integration rank, sample size, stationary dynamics and models of heteroskedasticity. Of these the wild bootstrap procedure is perhaps the more reliable overall since it avoids a significant tendency seen in the BIC-based method to over-estimate the co-integration rank in relatively small sample sizes.