Bayesian forecast combination for VAR models∗

This paper proposes a Bayesian procedure for combining forecasts from multivariate forecasting models, e.g. VAR models. Standard applications of Bayesian model averaging suffer from a basic difficulty in this context, when additional variables are included and modelled the connection between the overall measure of fit for the model and the expected forecasting performance for the variables of interest is lost. We circumvent this problem by focusing on the predictive performance for the variables of interest and base the forecast combination on the predictive likelihood. Specifically we consider forecast combination and, indirectly, model selection for VAR models when there is uncertainty about which variables to include in the model in addition to the forecast variables. For this purpose we consider all possible combinations of variables and lag lengths and the models that arise from these. The procedure is evaluated in a small simulation study and found to perform competitively in applications to real world data.