Solving the Forecast Combination Puzzle

The forecast combination puzzle is the commonly encountered empirical result whereby predictions formed by combining multiple forecasts in complex ways do not out-perform more naive, e.g. equally-weighted, approaches. While various solutions for the cause of the puzzle exist in the literature, these solutions are limited in their scope and applicability. In contrast, we demonstrate a general solution to the puzzle by showing that this phenomenon is a direct consequence of the methodology used to produce forecast combinations. In particular, we show that tests which aim to discriminate between the predictive accuracy of competing forecast combination strategies have low power, and can lack size control, leading to an outcome that favours the naive approach. In addition, we demonstrate that the low power of such predictive accuracy tests in the forecast combination setting can be completely avoided if more efficient strategies are used in the production of the combinations. We illustrate these findings both in the context of forecasting a functional of interest and in terms of predictive densities. A short empirical example using daily financial returns exemplifies how researchers can avoid the puzzle in practical settings.