Predictive Density Combination Using a Tree-Based Synthesis Function

Bayesian predictive synthesis (BPS) is a method of combining predictive distributions based on agent opinion analysis theory, which encompasses many common approaches to combining density forecasts. The key ingredient in BPS is a synthesis function. This is typically specified parametrically as a dynamic linear regression. In this paper, we develop a nonparametric treatment of the synthesis function using regression trees. We show the advantages of our tree-based approach in two macroeconomic forecasting applications. The first uses density forecasts for GDP growth from the euro area’s Survey of Professional Forecasters. The second combines density forecasts of US inflation produced by many regression models involving different predictors. Both applications demonstrate the benefits—in terms of improved forecast accuracy and interpretability—of modeling the synthesis function nonparametrically.