Title: Forecast combining for multivariate probability distributions
Authors: Xiaochun Meng - University of Sussex (United Kingdom) [presenting]
James Taylor - University of Oxford (United Kingdom)
Abstract: The evolution of extreme temperature has significant implications for the ecosystem and society. Short-term forecasts of extreme temperature are needed to support decision-making in a variety of organisations. We first generate forecasts of the joint distribution of the daily minimum and maximum temperature using ARMA-GARCH models fitted to daily data. We then compare these predictions with those of a model fitted to hourly data. Rather than selecting between these approaches, we consider the combination of the distributional forecasts produced by each. Combining forecasts has been shown to be beneficial in many different contexts. The combination can be viewed as a synthesis of information, or as a portfolio of forecasts, where the aim is to diversify the forecast risk. Although there have been many methods proposed for combining point forecasts, there is only a small literature on combining distributional forecasts. Very few papers have considered the forecasting of multivariate distributions. We generalise methods previously proposed for combining forecasts of univariate distributions based on quantiles. This framework allows us to vary the combining weights over the outcome space. We use proper scoring functions to optimise the weights, and we evaluate the calibration and sharpness of the resulting forecasts using theoretical analysis, as well as an empirical study based on European temperature data.