A Simple Explanation of the Forecast Combination Puzzle*

TLDR

The forecast combination puzzle shows that simple point forecast combinations often outperform sophisticated weighted combinations in empirical studies. The study explains the puzzle by attributing it to finite‑sample error in estimating combining weights. The authors attribute the puzzle to finite‑sample error in weight estimation, supported by a small Monte Carlo experiment and a large‑sample variance approximation. The evidence confirms that ignoring forecast error covariances when estimating weights is justified and explains why simple combinations perform well. Citation: Fed.

Abstract

Abstract This article presents a formal explanation of the forecast combination puzzle, that simple combinations of point forecasts are repeatedly found to outperform sophisticated weighted combinations in empirical applications. The explanation lies in the effect of finite‐sample error in estimating the combining weights. A small Monte Carlo study and a reappraisal of an empirical study by Stock and Watson [ Federal Reserve Bank of Richmond Economic Quarterly (2003) Vol. 89/3, pp. 71–90] support this explanation. The Monte Carlo evidence, together with a large‐sample approximation to the variance of the combining weight, also supports the popular recommendation to ignore forecast error covariances in estimating the weight.