The Forecast Combination Puzzle: A Simple Theoretical Explanation

Gerda Claeskens, J.R. Magnus, Andrey L. Vasnev, Wendun Wang
2014 Social Science Research Network  
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
more » ... (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.
doi:10.2139/ssrn.2498475 fatcat:d4u5rlcipveytoziqbr5jotmla