Forecast combinations: an over 50-year review

TL;DR

This paper reviews over 50 years of research on forecast combinations, highlighting their evolution, methods, applications, and future research directions in improving forecast accuracy.

Contribution

It provides a comprehensive, up-to-date review of forecast combination methods, including recent advances and open-source software, identifying research gaps and future opportunities.

Findings

Forecast combinations improve accuracy by integrating diverse sources.

Methods have evolved from simple to sophisticated, including nonlinear and time-varying weights.

Forecast combinations are now central to mainstream forecasting research.

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 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.