A Simple Theoretical Explanation of the Forecast Combination Puzzle

This paper offers a theoretical explanation why forecast combination with the estimated optimal weights has often poor performance in applications. The explanation is simple. The properties of the combination are often derived under the assumption that the weights are fixed while in practice they have to be estimated. If the weight estimation is taken into account during the optimality derivation, the combination might be biased (even if the original forecasts are unbiased) and its variance is larger and no longer guaranteed to be an improvement upon the original forecasts. If normality does not hold, then the optimal weights can be different from the weights derived without taking the estimation step into account.