# The forecast combination puzzle: A simple theoretical explanation

Gerda Claeskens, Jan R. Magnus, Andrey L. Vasnev, Wendun Wang

### Abstract

This paper 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 will be larger than in the fixed-weight case. In particular, there is no guarantee that the 'optimal' forecast combination will be better than the equal-weight case, or even improve on the original forecasts. We provide the underlying theory, some special cases, and a numerical illustration.

Original language English 754-762 9 International Journal of Forecasting 32 3 https://doi.org/10.1016/j.ijforecast.2015.12.005 Published - 2016

### Fingerprint

Forecast combination
Optimality
Guarantee
Stylized facts

### Keywords

• Forecast combination
• Optimal weights

### Cite this

Claeskens, Gerda ; Magnus, Jan R. ; Vasnev, Andrey L. ; Wang, Wendun. / The forecast combination puzzle : A simple theoretical explanation. In: International Journal of Forecasting. 2016 ; Vol. 32, No. 3. pp. 754-762.
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The forecast combination puzzle : A simple theoretical explanation. / Claeskens, Gerda; Magnus, Jan R.; Vasnev, Andrey L.; Wang, Wendun.

In: International Journal of Forecasting, Vol. 32, No. 3, 2016, p. 754-762.

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AU - Magnus, Jan R.

AU - Vasnev, Andrey L.

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AB - This paper 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 will be larger than in the fixed-weight case. In particular, there is no guarantee that the 'optimal' forecast combination will be better than the equal-weight case, or even improve on the original forecasts. We provide the underlying theory, some special cases, and a numerical illustration.

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