A0925
Title: Angular combining of forecasts of probability distributions: Applications and developments
Authors: James Taylor - University of Oxford (United Kingdom) [presenting]
Xiaochun Meng - University of Bath (United Kingdom)
Abstract: To enable a pragmatic synthesis of the information available in different forecasts of a probability distribution, forecast combining can be used. The combination has often been applied to the probability predictions of the distributional forecasts. However, it has been suggested that this will tend to deliver overdispersed distributional forecasts, prompting the combination to be applied instead to the quantile predictions. The probability combining approach can be viewed as vertical combining of the probability distributions, and the quantile combining approach is viewed as horizontal combining. The proposal is to combine at an angle between the extreme cases of vertical and horizontal combining, with the angle optimized using a proper scoring rule. For implementation, a pragmatic numerical approach and a simulation algorithm are provided. Among the theoretical results, it is shown that, as with vertical and horizontal averaging, angular averaging results in a distribution with a mean equal to the average of the means of the distributions that are being combined. It is also shown that angular averaging produces a distribution with lower variance than vertical averaging and, under certain assumptions, greater variance than horizontal averaging. An empirical illustration of angular combining using several different applications is provided. Finally, potential extensions and generalizations are described.
