Bayesian Inference in Cointegrated I (2) Systems: A Generalization of the Triangular Model

This paper generalizes the cointegrating model of Phillips (1991) to allow for I (0), I (1) and I (2) processes. The model has a simple form that permits a wider range of I (2) processes than are usually considered, including a more flexible form of polynomial cointegration. Further, the specification relaxes restrictions identified by Phillips (1991) on the I (1) and I (2) cointegrating vectors and restrictions on how the stochastic trends enter the system. To date there has been little work on Bayesian I (2) analysis and so this paper attempts to address this gap in the literature. A method of Bayesian inference in potentially I (2) processes is presented with application to Australian money demand using a Jeffreys prior and a shrinkage prior.