Optimal Density Forecast Combinations

How should researchers combine predictive densities to improve their forecasts? I propose consistent estimators of weights which deliver density forecast combinations approximating the true predictive density, conditional on the researcher’s information set. Monte Carlo simulations confi rm that the proposed methods work well for sample sizes of practical interest. In an empirical example of forecasting monthly US industrial production, I demonstrate that the estimator delivers density forecasts which are superior to well-known benchmarks, such as the equal weights scheme. Specifi cally, I show that housing permits had valuable predictive power before and after the Great Recession. Furthermore, stock returns and corporate bond spreads proved to be useful predictors during the recent crisis, suggesting that fi nancial variables help with density forecasting in a highly leveraged economy.