Constructing Optimal Density Forecasts from Point Forecast Combinations

Decision makers often observe point forecasts of the same variable computed, for instance, by commercial banks, IMF, World Bank, but the econometric models used by such institutions are unknown. This paper shows how to use the information available at point forecasts to compute optimal density forecasts. Our idea builds upon the combination of point forecasts under general loss functions and unknonwn forecast error distributions. We use real-time data to forecast the density of future in‡ation in the U.S. and our results indicate that the proposed method materially improves the real-time accuracy of density forecasts vis-à-vis the ones obtained from the (unknown) individual. econometric models.