Cointegration in a periodic vector autoregression

We consider representation, estimation and inference on cointegration in a (PVAR). We show that cointegration amounts to a restriction on a product of parameter matrices. We therefore use GMM to construct estimators of the long-run (cointegration) parameters and to obtain test statistics for cointegration. We show that the limiting distributions of the GMM estimators and the corresponding test statistics in a PVAR are identical to those of the maximum likelihood cointegration estimators and test statistics in standard nonperiodic VAR models.