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 can be obtained by averaging the individual parameters. This paper 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. In general we find that: (i) larger differences among the combination schemes occur when there are biases in the individual forecasts, in which case quantile aggregation seems preferable overall; (ii) the choice of the combination weights is important in determining the performance of the various methods. Monte Carlo simulation experiments indicate that the properties of quantile aggregation fall between those of the linear and the logarithmic pool, and that quantile averaging is particularly useful for combining forecast distributions with large differences in location. An empirical illustration is provided with density forecasts from time series and econometric models for Italian GDP.