Forecast Combination and Model Averaging Using Predictive Measures

We extend the standard approach to Bayesian forecast combination by forming the weights for the model averaged forecast from the predictive likelihood rather than the standard marginal likelihood. The use of predictive measures of fit offers greater protection against in-sample overfitting and improves forecast performance. For the predictive likelihood we show analytically that the forecast weights have good large and small sample properties. This is confirmed in a simulation study and an application to forecasts of the Swedish inflation rate where forecast combination using the predictive likelihood outperforms standard Bayesian model averaging using the marginal likelihood.