Bayesian Prediction Based on the Cointegrated Vector Autoregression

Mattias Villani

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 choice of cointegration vectors 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 distribution. The ideas of Litterman are adapted for the prior on the short run dynamics of the process 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 a focus on forecasting the Swedish inflation.
Keywords: Bayesian, Cointegration, Inflation forecasting, Model averaging, Predictive density.

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