Bayesian analysis of seasonally cointegrated VAR models

Abstract

The aim is to develop a Bayesian seasonally cointegrated model for quarterly data. Relevant prior structure is proposed, and the set of full conditional posterior distributions is derived, enabling us to employ the Gibbs sampler for posterior inference. The identification of cointegrating spaces is obtained by orthonormality restrictions imposed on vectors spanning them. The point estimation of the cointegrating spaces is also discussed. In the presence of a seasonal pattern with one cycle per year, the cointegrating vectors belong to the complex space, which should be taken into account in the identification scheme. The methodology is illustrated by the analysis of money and prices in the Polish economy.