Bayesian Prediction with a Cointegrated Vector Autoregression

A complete procedure for calculating the joint predictive distribution of future observations based on the cointegrated vector autoregression is presented. The large degree of uncertainty in the choise of the cointegration vectors is incorporated into the analysis through a prior distribution on the cointegration vectors which allows the forecaster to realistically express his beliefs. This prior leads to a form of model averaging where the predictions from the models based on the different cointegration vectors are weighted together in an optimal way. The ideas of Litterman (1980) are adapted for the prior on the short run dynamics with a resulting prior which only depends on a few hyperparameters and is therefore easily specified. A straight forward numerical evaluation of the predictive distribution based on Gibbs sampling is proposed. The prediction procedure is applied to a seven variable system with focus on forecasting the Swedish inflation.