Testing for Cointegration Rank Using Bayes Factors

This paper proposes Bayesian methods for estimating the cointegration rank in an automatic way using Bayes factors. First, we consider natural conjugate priors for computing Bayes factors for the adjustment term. Since using conjugate priors requires that we assign the prior parameters of which we often do not have prior information, and testing by Bayes factor is very sensitive to the parameters, we propose in this paper using the maximum likelihood estimators for the prior parameters. Then, we show the case of using non-informative priors. Since normal Bayes factor cannot be computed with non-informative priors, we apply the intrinsic Bayes factor (IBF) proposed by Berger and Pericchi (1996). Monte Carlo simulations show that using Bayes factor with conjugate priors and the IBF with non-informative priors produce fairly good results. The methods proposed here are also applied for selecting the appropriate lags, or other tests for a VAR model.