Solving the Forecasting Combination Puzzle

Abstract
We demonstrate that the so-called forecasting combination puzzle is a consequence of the methodology commonly used to produce forecast combinations. By the combination puzzle, we refer to the empirical finding that predictions formed by combining multiple forecasts in ways that seek to optimize forecast performance often do not out-perform more naive, e.g. equally-weighted, approaches. In particular, we demonstrate that, due to the manner in which such forecasts are typically produced, tests that aim to discriminate between the predictive accuracy of such competing combinations can have low power, and can lack size control, leading to an outcome that favors the simpler approach. In short, we show that this counter-intuitive result can be completely avoided by the adoption of more efficient estimation strategies in the production of the combinations, when feasible. We illustrate these findings both in the context of forecasting a functional of interest and in terms of predictive densities. Joint paper with Ryan Zischke, Gael M. Martin and Donald Poskitt.