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 and the World Bank, but the econometric models used by such institutions are frequently unknown. This paper shows how to use the information available on point forecasts to compute optimal density forecasts. Our idea builds upon the combination of point forecasts under general loss functions and unknown forecast error distributions. We use real-time data to forecast the density of US inflation. The results indicate that the proposed method materially improves the real-time accuracy of density forecasts vis-à-vis those from the (unknown) individual econometric models.