A numerical bayesian test for cointegration of AR processes

Bayesian Monte Carlo techniques are used to develop a posterior odds ratio test for cointegration which centers directly on the system dynamics implied by the model parameters — in particular on the number of nonstationary roots in the system. The procedure accounts for prior information concerning the probability of cointegration, the order of integration of the individual series, and the lag length necessary to model the series. An empirical example is provided using a set of foreign exchange rates. The posterior odds show little support for cointegration among the exchange rates tested.