The forecast combination puzzle: A simple theoretical explanation

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract: This papers 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 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 an application in the context of model selection. Terms of use: Documents in

Forecast Combinations in R using the ForecastComb Package

“…A rigorous attempt to explain why simple average weights often outperform more sophisticated forecast combination techniques is provided in a simulation study by Smith and Wallis (2009), who ascribe this surprising empirical finding to the effect of finite-sample error in estimating the combination weights. Recently, Claeskens et al (2016) provide a theoretical argumentation to these empirical findings. The authors make the case that lower estimation noise, when the weights are determined rather than estimated, goes a long way in explaning the puzzle.…”

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A Forecast Combination Framework with Multi‐Time Scale for Livestock Products’ Price Forecasting

“…In our research, ω 1 � ω 2 � 0.5. Although it seems quite simple, compared with other complex weighting schemes, it is usually regarded as a robust method especially in the real prediction circumstance [24,26].…”

“…Suppose the forecasts from two individual models are unbiased, with σ 2 1 and σ 2 2 as their individual variance, and σ 12 as their covariance. By minimizing the variance of forecasts, the optimal weights will then be written as [24]…”

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