The Forecast Combination Puzzle: A Simple Theoretical Explanation
22 Pages Posted: 5 Mar 2016
Date Written: February 2016
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.
Keywords: forecast combination, optimal weights
JEL Classification: C53, C52
Suggested Citation: Suggested Citation