Co†integration Rank Determination in Partial Systems Using Information Criteria

We investigate the asymptotic and finite sample properties of the most widely used information criteria for co†integration rank determination in ‘partial’ systems, i.e. in co†integrated vector autoregressive (VAR) models where a sub†set of variables of interest is modelled conditional on another sub†set of variables. The asymptotic properties of the Akaike information criterion (AIC), the Bayesian information criterion (BIC) and the Hannan–Quinn information criterion (HQC) are established, and consistency of BIC and HQC is proved. Notably, the consistency of BIC and HQC is robust to violations of weak exogeneity of the conditioning variables with respect to the co†integration parameters. More precisely, BIC and HQC recover the true co†integration rank from the partial system analysis also when the conditional model does not convey all information about the co†integration parameters. This result opens up interesting possibilities for practitioners who can now determine the co†integration rank in partial systems without being concerned about the weak exogeneity of the conditioning variables. A Monte Carlo experiment based on a large dimensional data generating process shows that BIC and HQC applied in partial systems perform reasonably well in small samples and comparatively better than ‘traditional’ methods for co†integration rank determination. We further show the usefulness of our approach and the benefits of the conditional system analysis in two empirical illustrations, both based on the estimation of VAR systems on US quarterly data. Overall, our analysis shows the gains of combining information criteria with partial system analysis.