The forecast combination puzzle

This paper offers a theoretical explanation for the stylized fact that forecast combinations with estimated optimal weights often perform poorly in applications. The properties of the forecast combination are typically derived under the assumption that the weights are fixed, while in practice they need to be estimated. If the fact that the weights are random rather than fixed is taken into account during the optimality derivation, then the forecast combination will be biased (even when the original forecasts are unbiased) and its variance is larger than in the fixed-weights case. In particular, there is no guarantee that the ‘optimal’ forecast combination will be better than the equal-weights case or even improve on the original forecasts. We provide the underlying theory, some special cases, and a numerical illustration. publisher: Elsevier articletitle: The forecast combination puzzle: A simple theoretical explanation journaltitle: International Journal of Forecasting articlelink: http://dx.doi.org/10.1016/j.ijforecast.2015.12.005 content_type: article copyright: Crown Copyright © 2016 Published by Elsevier B.V. on behalf of International Institute of Forecasters. All rights reserved. ispartof: International Journal of Forecasting vol:32 issue:3 pages:754-762 status: published