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A Combination Method for Averaging OLS and GLS Estimators

On the Forecast Combination Puzzle

Department of Applied Economics and Statistics, University of Delaware, Newark, DE 19716, USA
School of Statistics, University of Minnesota, Minneapolis, MN 55455, USA
Author to whom correspondence should be addressed.
Econometrics 2019, 7(3), 39;
Received: 15 June 2019 / Revised: 29 August 2019 / Accepted: 6 September 2019 / Published: 10 September 2019
(This article belongs to the Special Issue Bayesian and Frequentist Model Averaging)
It is often reported in the forecast combination literature that a simple average of candidate forecasts is more robust than sophisticated combining methods. This phenomenon is usually referred to as the “forecast combination puzzle”. Motivated by this puzzle, we explore its possible explanations, including high variance in estimating the target optimal weights (estimation error), invalid weighting formulas, and model/candidate screening before combination. We show that the existing understanding of the puzzle should be complemented by the distinction of different forecast combination scenarios known as combining for adaptation and combining for improvement. Applying combining methods without considering the underlying scenario can itself cause the puzzle. Based on our new understandings, both simulations and real data evaluations are conducted to illustrate the causes of the puzzle. We further propose a multi-level AFTER strategy that can integrate the strengths of different combining methods and adapt intelligently to the underlying scenario. In particular, by treating the simple average as a candidate forecast, the proposed strategy is shown to reduce the heavy cost of estimation error and, to a large extent, mitigate the puzzle. View Full-Text
Keywords: combining for adaptation; combining for improvement; multi-level AFTER; model selection; structural break combining for adaptation; combining for improvement; multi-level AFTER; model selection; structural break
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MDPI and ACS Style

Qian, W.; Rolling, C.A.; Cheng, G.; Yang, Y. On the Forecast Combination Puzzle. Econometrics 2019, 7, 39.

AMA Style

Qian W, Rolling CA, Cheng G, Yang Y. On the Forecast Combination Puzzle. Econometrics. 2019; 7(3):39.

Chicago/Turabian Style

Qian, Wei, Craig A. Rolling, Gang Cheng, and Yuhong Yang. 2019. "On the Forecast Combination Puzzle" Econometrics 7, no. 3: 39.

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