Quantile-adaptive probabilistic forecast combining

Combining forecasts of cumulative probability distributions (CDFs) allows aggregation of the available information to improve accuracy. The linear opinion pool is commonly used, but it can yield overdispersed distributional forecasts. An alternative, leading to lower dispersion, is to average the quantiles of the CDF, which can be viewed as horizontal CDF averaging, with the averaging of probabilities in the linear opinion pool viewed as vertical averaging. Empirical results show that horizontal and vertical averaging can each be preferable for different parts of the CDF. For example, one method might be better for tail quantiles, while the other is better for central quantiles. To address this, we develop a method that transitions between vertical and horizontal averaging across the CDF. It relates to angular averaging, which is a recent proposal that performs aggregation along lines at an angle. Our new method averages along lines with slopes that smoothly transition across the CDF. The method is quantile-adaptive in the sense that the slopes of the lines vary across the quantiles, or equivalently, across the probabilities. We set the lines to emanate from a small number of fixed points, which are the parameters of the method. Viewing the lines as rays, we term the method radial averaging. Our theoretical results show that the method has the versatility to generate CDF forecasts that are sharper than horizontal averaging, and less sharp than vertical averaging. Our empirical results provide support for the new approach.