Modeling multivariate co integrated systems: Insights from non‐linear dynamics

Johansen's test for co integration is applied to Litterman's original six‐variable Bayesian vector auto regression (BVAR) model to obtain vector error correction mechanism (VECM) and Bayesian error correction (BECM) versions of the model. The Brock, Dechert, and Scheinkman (BDS) test for independence from the non‐linear dynamics literature is then applied to the error structures of each estimated equation of the BECM and VECM models, plus two BVAR versions of the model. The results show that none of the models produce independent and identically distributed (IID) errors for all six equations. However, the BDS results suggest the elimination of the Bayesian prior from the BECM model, given that the univariate VECM errors are IID in five equations, compared to only two or three equations under the three Bayesian restricted models. These results combined with previous evidence regarding the superior forecasting performance of BECM over ECM models suggest future experimentation with less restrictive BVAR priors, BECM models corrected for heteroscedasticity, or hybrid specifications based on the nonlinear dynamics literature.