Cointegration in Multivariate Periodic Time Series Models.

In this paper we extend the univariate periodic integration model to multivariate cointegrated time series. We analyze representation issues of a multivariate periodic model. We argue that simple adding an index s to the parameters in an otherwise nonperiodic Vector AutoRegression (VAR) leads to a model representation which is hard to analyze for cointegration. Therefore, we propose an alternative Periodic VAR (PVAR) representation, which is much more convenient for our purposes. We show that cointegration amounts to a restriction on a product of parameter matrices. We use GMM to construct estimators of the long run (cointegration) parameters and also test statistics for cointegration. We find that the limiting distributions of our GMM estimators and test statistics for cointegration. We find that the limiting distributions of our GMM estimators and test statistics in standard VAR Models.