Quantile Aggregation of Density Forecasts

Quantile aggregation (or ‘Vincentization’) is a simple and intuitive way of combining probability distributions, originally proposed by S.B. Vincent in 1912. In certain cases, such as under Gaussianity, the Vincentized distribution belongs to the same family as that of the individual distributions and it can be obtained by averaging the individual parameters. This article compares the properties of quantile aggregation with those of the forecast combination schemes normally adopted in the econometric forecasting literature, based on linear or logarithmic averages of the individual densities. Analytical results and Monte Carlo experiments indicate that the properties of quantile aggregation are between those of the linear and the logarithmic pool. Larger differences among the combination schemes occur when there are biases in the individual forecasts: in that case quantile aggregation seems preferable on the whole. The practical usefulness of Vincentization is illustrated empirically in the context of linear forecasting models for Italian GDP and quantile predictions of euro area inflation.