Forecast combinations: an over 50-year review

Abstract

Forecast combinations have flourished remarkably in the forecasting community and, in recent years, have become part of the mainstream of forecasting research and activities. Combining multiple forecasts produced from the single (target) series is now widely used to improve accuracy through the integration of information gleaned from different sources, thereby mitigating the risk of identifying a single "best" forecast. Combination schemes have evolved from simple combination methods without estimation, to sophisticated methods involving time-varying weights, nonlinear combinations, correlations among components, and cross-learning. They include combining point forecasts, and combining probabilistic forecasts. This paper provides an up-to-date review of the extensive literature on forecast combinations, together with reference to available open-source software implementations. We discuss the potential and limitations of various methods and highlight how these ideas have developed over time. Some important issues concerning the utility of forecast combinations are also surveyed. Finally, we conclude with current research gaps and potential insights for future research.

The Impact of Sampling Variability on Estimated Combinations of Distributional Forecasts

“…Since the publication of the seminal papers by Stone (1961) and Bates and Granger (1969), the forecasting literature has seen an explosion of interest in the production of point and/or distributional forecasts via weighted combinations of forecasts from distinct models (see Timmermann 2006, Aastveit et al 2019, and Wang et al 2022 for relevant reviews). Forecast combinations (of both types) have attracted such attention in part because of their highly competitive performance out-of-sample (Makridakis et al 2018(Makridakis et al , 2020Thorey et al 2018;Wang et al 2018;Taylor 2020).…”