Bayesian prediction with cointegrated vector autoregressions

A complete procedure for calculating the joint predictive distribution of f uture observations based on the cointegrated vector autoregression is prese nted. The large degree of uncertainty in the choice of cointegration vector s is incorporated into the analysis via the prior distribution. This prior has the effect of weighing the predictive distributions based on the models with different cointegration vectors into an overall predictive distributi on. The ideas of Litterman [Mimeo, Massachusetts Institute of Technology, 1 980] are adopted for the prior on the short run dynamics of the process res ulting in a prior which only depends on a few hyperparameters. A straightfo rward numerical evaluation of the predictive distribution based on Gibbs sa mpling is proposed. The prediction procedure is applied to a seven-variable system with a focus on forecasting Swedish inflation. (C) 2001 Elsevier Sc ience B.V. All rights reserved.