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Quantile aggregation of density forecasts

Author

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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

    as
    1. Kapetanios, G. & Mitchell, J. & Price, S. & Fawcett, N., 2015. "Generalised density forecast combinations," Journal of Econometrics, Elsevier, vol. 188(1), pages 150-165.
    2. Billio, Monica & Casarin, Roberto & Ravazzolo, Francesco & van Dijk, Herman K., 2013. "Time-varying combinations of predictive densities using nonlinear filtering," Journal of Econometrics, Elsevier, vol. 177(2), pages 213-232.
    3. repec:wrk:wrkemf:05 is not listed on IDEAS
    4. Anne Sofie Jore & James Mitchell & Shaun P. Vahey, 2010. "Combining forecast densities from VARs with uncertain instabilities," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(4), pages 621-634.
    5. Malte Knüppel, 2015. "Evaluating the Calibration of Multi-Step-Ahead Density Forecasts Using Raw Moments," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(2), pages 270-281, April.
    6. Kenneth Wallis, 2011. "Combining forecasts - forty years later," Applied Financial Economics, Taylor & Francis Journals, vol. 21(1-2), pages 33-41.
    7. Granger, C. W. J. & White, Halbert & Kamstra, Mark, 1989. "Interval forecasting : An analysis based upon ARCH-quantile estimators," Journal of Econometrics, Elsevier, vol. 40(1), pages 87-96, January.
    8. Corradi, Valentina & Swanson, Norman R., 2006. "Bootstrap conditional distribution tests in the presence of dynamic misspecification," Journal of Econometrics, Elsevier, vol. 133(2), pages 779-806, August.
    9. Del Negro, Marco & Hasegawa, Raiden B. & Schorfheide, Frank, 2016. "Dynamic prediction pools: An investigation of financial frictions and forecasting performance," Journal of Econometrics, Elsevier, vol. 192(2), pages 391-405.
    10. Tilmann Gneiting & Roopesh Ranjan, 2011. "Comparing Density Forecasts Using Threshold- and Quantile-Weighted Scoring Rules," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(3), pages 411-422, July.
    11. Waggoner, Daniel F. & Zha, Tao, 2012. "Confronting model misspecification in macroeconomics," Journal of Econometrics, Elsevier, vol. 171(2), pages 167-184.
    12. Michael P. Clements, 2004. "Evaluating the Bank of England Density Forecasts of Inflation," Economic Journal, Royal Economic Society, vol. 114(498), pages 844-866, October.
    13. Geweke, John & Amisano, Gianni, 2011. "Optimal prediction pools," Journal of Econometrics, Elsevier, vol. 164(1), pages 130-141, September.
    14. A. E. Faria & E. Mubwandarikwa, 2008. "The geometric combination of Bayesian forecasting models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 27(6), pages 519-535.
    15. Dr. James Mitchell, 2005. "Evaluating, comparing and combining density forecasts using the KLIC with an application to the Bank of England and NIESR ÔfanÕ charts of inflation," National Institute of Economic and Social Research (NIESR) Discussion Papers 253, National Institute of Economic and Social Research.
    16. Fabio Busetti & Pietro Cova, 2013. "The macroeconomic impact of the sovereign debt crisis: a counterfactual analysis for the Italian economy," Questioni di Economia e Finanza (Occasional Papers) 201, Bank of Italy, Economic Research and International Relations Area.
    17. Christoffersen, Peter F. & Diebold, Francis X., 1997. "Optimal Prediction Under Asymmetric Loss," Econometric Theory, Cambridge University Press, vol. 13(6), pages 808-817, December.
    18. David F. Hendry & Michael P. Clements, 2004. "Pooling of forecasts," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 1-31, June.
    19. Stephen G. Hall & James Mitchell, 2009. "Recent Developments in Density Forecasting," Palgrave Macmillan Books, in: Terence C. Mills & Kerry Patterson (ed.), Palgrave Handbook of Econometrics, chapter 5, pages 199-239, Palgrave Macmillan.
    20. Hall, Stephen G. & Mitchell, James, 2007. "Combining density forecasts," International Journal of Forecasting, Elsevier, vol. 23(1), pages 1-13.
    21. Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-883, November.
    22. Christian Kascha & Francesco Ravazzolo, 2010. "Combining inflation density forecasts," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 29(1-2), pages 231-250.
    23. Kenneth C. Lichtendahl & Yael Grushka-Cockayne & Robert L. Winkler, 2013. "Is It Better to Average Probabilities or Quantiles?," Management Science, INFORMS, vol. 59(7), pages 1594-1611, July.
    24. Amisano, Gianni & Giacomini, Raffaella, 2007. "Comparing Density Forecasts via Weighted Likelihood Ratio Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 177-190, April.
    25. Kenneth F. Wallis, 2005. "Combining Density and Interval Forecasts: A Modest Proposal," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 67(s1), pages 983-994, December.
    26. Gneiting, Tilmann & Ranjan, Roopesh, 2011. "Comparing Density Forecasts Using Threshold- and Quantile-Weighted Scoring Rules," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(3), pages 411-422.
    27. Dr. James Mitchell, 2005. "Evaluating, comparing and combining density forecasts using the KLIC with an application to the Bank of England and NIESR ÔfanÕ charts of inflation," National Institute of Economic and Social Research (NIESR) Discussion Papers 253, National Institute of Economic and Social Research.
    28. G. Elliott & C. Granger & A. Timmermann (ed.), 2006. "Handbook of Economic Forecasting," Handbook of Economic Forecasting, Elsevier, edition 1, volume 1, number 1.
    29. James Mitchell & Stephen G. Hall, 2005. "Evaluating, Comparing and Combining Density Forecasts Using the KLIC with an Application to the Bank of England and NIESR ‘Fan’ Charts of Inflation," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 67(s1), pages 995-1033, December.
    30. Corradi, Valentina & Swanson, Norman R., 2006. "Predictive Density Evaluation," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 5, pages 197-284, Elsevier.
    31. 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.
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    Cited by:

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    6. Wang, Shengjie & Kang, Yanfei & Petropoulos, Fotios, 2024. "Combining probabilistic forecasts of intermittent demand," European Journal of Operational Research, Elsevier, vol. 315(3), pages 1038-1048.
    7. 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.
    8. 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.
    9. Diebold, Francis X. & Shin, Minchul & Zhang, Boyuan, 2023. "On the aggregation of probability assessments: Regularized mixtures of predictive densities for Eurozone inflation and real interest rates," Journal of Econometrics, Elsevier, vol. 237(2).
    10. 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.
    11. Ray, Evan L. & Brooks, Logan C. & Bien, Jacob & Biggerstaff, Matthew & Bosse, Nikos I. & Bracher, Johannes & Cramer, Estee Y. & Funk, Sebastian & Gerding, Aaron & Johansson, Michael A. & Rumack, Aaron, 2023. "Comparing trained and untrained probabilistic ensemble forecasts of COVID-19 cases and deaths in the United States," International Journal of Forecasting, Elsevier, vol. 39(3), pages 1366-1383.
    12. Yoonseok Lee & Donggyu Sul, 2023. "Depth-weighted Forecast Combination: Application to COVID-19 Cases," Advances in Econometrics, in: Essays in Honor of Joon Y. Park: Econometric Methodology in Empirical Applications, volume 45, pages 235-260, Emerald Group Publishing Limited.
    13. 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.
    14. Makariou, Despoina & Barrieu, Pauline & Tzougas, George, 2021. "A finite mixture modelling perspective for combining experts’ opinions with an application to quantile-based risk measures," LSE Research Online Documents on Economics 110763, London School of Economics and Political Science, LSE Library.
    15. Ryan Cumings-Menon & Minchul Shin, 2020. "Probability Forecast Combination via Entropy Regularized Wasserstein Distance," Working Papers 20-31/R, Federal Reserve Bank of Philadelphia.
    16. 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.
    17. Berrisch, Jonathan & Ziel, Florian, 2023. "CRPS learning," Journal of Econometrics, Elsevier, vol. 237(2).
    18. 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.
    19. Wang, Xiaoqian & Hyndman, Rob J. & Li, Feng & Kang, Yanfei, 2023. "Forecast combinations: An over 50-year review," International Journal of Forecasting, Elsevier, vol. 39(4), pages 1518-1547.

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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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