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Quantile aggregation of density forecasts

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  • Fabio Busetti

    (Bank of Italy)

Abstract

Quantile aggregation (or 'Vincentization') is a simple and intuitive way of combining probability distributions, originally proposed by S. B. Vincent in 1912. In certain cases, such as under Gaussianity, the Vincentized distribution belongs to the same family as that of the individual distributions and can be obtained by averaging the individual parameters. This paper compares the properties of quantile aggregation with those of the forecast combination schemes normally adopted in the econometric forecasting literature, based on linear or logarithmic averages of the individual densities. In general we find that: (i) larger differences among the combination schemes occur when there are biases in the individual forecasts, in which case quantile aggregation seems preferable overall; (ii) the choice of the combination weights is important in determining the performance of the various methods. Monte Carlo simulation experiments indicate that the properties of quantile aggregation fall between those of the linear and the logarithmic pool, and that quantile averaging is particularly useful for combining forecast distributions with large differences in location. An empirical illustration is provided with density forecasts from time series and econometric models for Italian GDP.

Suggested Citation

  • Fabio Busetti, 2014. "Quantile aggregation of density forecasts," Temi di discussione (Economic working papers) 979, Bank of Italy, Economic Research and International Relations Area.
  • Handle: RePEc:bdi:wptemi:td_979_14
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    References listed on IDEAS

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    2. Julien Randon-Furling & Madalina Olteanu & Antoine Lucquiaud, 2020. "From urban segregation to spatial structure detection," Environment and Planning B, , vol. 47(4), pages 645-661, May.
    3. Jonathan Berrisch & Florian Ziel, 2021. "CRPS Learning," Papers 2102.00968, arXiv.org, revised Nov 2021.
    4. Busetti, Fabio & Caivano, Michele & Delle Monache, Davide & Pacella, Claudia, 2021. "The time-varying risk of Italian GDP," Economic Modelling, Elsevier, vol. 101(C).
    5. Laporta, Alessandro G. & Merlo, Luca & Petrella, Lea, 2018. "Selection of Value at Risk Models for Energy Commodities," Energy Economics, Elsevier, vol. 74(C), pages 628-643.
    6. Ryan Cumings-Menon & Minchul Shin, 2020. "Probability Forecast Combination via Entropy Regularized Wasserstein Distance," Working Papers 20-31/R, Federal Reserve Bank of Philadelphia.
    7. Kathryn S Taylor & James W Taylor, 2022. "Interval forecasts of weekly incident and cumulative COVID-19 mortality in the United States: A comparison of combining methods," PLOS ONE, Public Library of Science, vol. 17(3), pages 1-25, March.
    8. Fabio Busetti & Michele Caivano & Lisa Rodano, 2015. "On the conditional distribution of euro area inflation forecast," Temi di discussione (Economic working papers) 1027, Bank of Italy, Economic Research and International Relations Area.
    9. Malte Knüppel & Fabian Krüger, 2022. "Forecast uncertainty, disagreement, and the linear pool," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(1), pages 23-41, January.
    10. Fabio Busetti & Michele Caivano & Davide Delle Monache, 2021. "Domestic and Global Determinants of Inflation: Evidence from Expectile Regression," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 83(4), pages 982-1001, August.
    11. Lorenzo Burlon & Simone Emiliozzi & Alessandro Notarpietro & Massimiliano Pisani, 2015. "Medium-term forecasting of euro-area macroeconomic variables with DSGE and BVARX models," Questioni di Economia e Finanza (Occasional Papers) 257, Bank of Italy, Economic Research and International Relations Area.
    12. Yoonseok Lee & Donggyu Sul, 2021. "Depth-Weighted Forecast Combination: Application to COVID-19 Cases," Center for Policy Research Working Papers 238, Center for Policy Research, Maxwell School, Syracuse University.
    13. Knut Are Aastveit & James Mitchell & Francesco Ravazzolo & Herman van Dijk, 2018. "The Evolution of Forecast Density Combinations in Economics," Tinbergen Institute Discussion Papers 18-069/III, Tinbergen Institute.
    14. Despoina Makariou & Pauline Barrieu & George Tzougas, 2021. "A Finite Mixture Modelling Perspective for Combining Experts’ Opinions with an Application to Quantile-Based Risk Measures," Risks, MDPI, vol. 9(6), pages 1-25, June.

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    More about this item

    Keywords

    Fan charts; macroeconomic forecasts; model combination.;
    All these keywords.

    JEL classification:

    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • E17 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Forecasting and Simulation: Models and Applications

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