Recalibrated Opinion Pools

This paper develops methods for combining density forecasts which accommodate stochastic dependence between dierent forecasters' predictions. Previous work combining density forecasts, using so-called "opinion pools", has essentially ignored dependence. The proposed basis for modelling the dependence among different forecasters' densities is a recalibration function, based on the probability integral transforms of the component densities. This reduces to a copula function in a special case. We explore the properties of various  approximations to the re-calibration function in Monte-Carlo simulations and in an application density forecasting UK GDP growth using the Bank of Englands "fan" chart for inflation. We find that the recalibrated opinion pool can deliver more accurate densities than traditional linear and logarithmic opinion pools in many realistic situations.