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The Impact of Sampling Variability on Estimated Combinations of Distributional Forecasts

Ryan Zischke, Gael M. Martin, David T. Frazier, D. S. Poskitt

arXiv 6 Jun 2022 · Statistics — Methodology · 2 citations (OpenAlex)

arXiv:2206.02376 · PDF · DOI · OpenAlex · Extracted main text

Abstract

We investigate the performance and sampling variability of estimated forecast combinations, with particular attention given to the combination of forecast distributions. Unknown parameters in the forecast combination are optimized according to criterion functions based on proper scoring rules, which are chosen to reward the form of forecast accuracy that matters for the problem at hand, and forecast performance is measured using the out-of-sample expectation of said scoring rule. Our results provide novel insights into the behavior of estimated forecast combinations. Firstly, we show that, asymptotically, the sampling variability in the performance of standard forecast combinations is determined solely by estimation of the constituent models, with estimation of the combination weights contributing no sampling variability whatsoever, at first order. Secondly, we show that, if computationally feasible, forecast combinations produced in a single step -- in which the constituent model and combination function parameters are estimated jointly -- have superior predictive accuracy and lower sampling variability than standard forecast combinations -- where constituent model and combination function parameters are estimated in two steps. These theoretical insights are demonstrated numerically, both in simulation settings and in an extensive empirical illustration using a time series of S&P500 returns.

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Gneiting \ Raftery (2007) Strictly Proper Scoring Rules, Prediction, and Estimation1.00073100%
2Martin, Loaiza-Maya, Maneesoonthorn, Frazier \ Ramŕez-Hassan (2022) Optimal Probabilistic Forecasts: When do They Work?1.00053100%
3Pagan (1986) Two Stage and Related Estimators and Their Applications0.92843100%
4Geweke \ Amisano (2011) Optimal Prediction Pools0.81142100%
5Newey \ McFadden (1994) Large Sample Estimation and Hypothesis Testing0.7946450%
6Gneiting \ Ranjan (2013) Combining Predictive Distributions0.73732100%
7Hall \ Mitchell (2007) Combining Density Forecasts0.73732100%
8Stock \ Watson (2004) Combination Forecasts of Output Growth in a Seven-Country Data Set0.73732100%
9van der Vaart (1998) Asymptotic Statistics, 32 Avenue of the Americas, New York, NY 10013-2473, USA: Cambridge University Press0.73732100%
10Smith \ Wallis (2009) A Simple Explanation of the Forecast Combination Puzzle0.64441100%

Showing the top 10 of 47 scored citations.