IDEAS home Printed from https://ideas.repec.org/p/bdi/wptemi/td_979_14.html
   My bibliography  Save this paper

Quantile aggregation of density forecasts

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.bancaditalia.it/pubblicazioni/temi-discussione/2014/2014-0979/en_tema_979.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    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. 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.
    4. 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.
    5. Kenneth Wallis, 2011. "Combining forecasts - forty years later," Applied Financial Economics, Taylor & Francis Journals, vol. 21(1-2), pages 33-41.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Waggoner, Daniel F. & Zha, Tao, 2012. "Confronting model misspecification in macroeconomics," Journal of Econometrics, Elsevier, vol. 171(2), pages 167-184.
    11. 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.
    12. Geweke, John & Amisano, Gianni, 2011. "Optimal prediction pools," Journal of Econometrics, Elsevier, vol. 164(1), pages 130-141, September.
    13. 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.
    14. 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.
    15. 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.
    16. Christoffersen, Peter F. & Diebold, Francis X., 1997. "Optimal Prediction Under Asymmetric Loss," Econometric Theory, Cambridge University Press, vol. 13(6), pages 808-817, December.
    17. David F. Hendry & Michael P. Clements, 2004. "Pooling of forecasts," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 1-31, June.
    18. 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.
    19. Hall, Stephen G. & Mitchell, James, 2007. "Combining density forecasts," International Journal of Forecasting, Elsevier, vol. 23(1), pages 1-13.
    20. 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.
    21. Christian Kascha & Francesco Ravazzolo, 2010. "Combining inflation density forecasts," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 29(1-2), pages 231-250.
    22. 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.
    23. 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.
    24. 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.
    25. 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.
    26. 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.
    27. G. Elliott & C. Granger & A. Timmermann (ed.), 2006. "Handbook of Economic Forecasting," Handbook of Economic Forecasting, Elsevier, edition 1, volume 1, number 1.
    28. 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.
    29. 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.
    30. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Busetti, Fabio & Caivano, Michele & Delle Monache, Davide & Pacella, Claudia, 2021. "The time-varying risk of Italian GDP," Economic Modelling, Elsevier, vol. 101(C).
    6. 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.
    7. Berrisch, Jonathan & Ziel, Florian, 2023. "CRPS learning," Journal of Econometrics, Elsevier, vol. 237(2).
    8. Jonathan Berrisch & Florian Ziel, 2021. "CRPS Learning," Papers 2102.00968, arXiv.org, revised Nov 2021.
    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. 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.
    11. 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.
    12. 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.
    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. Ryan Cumings-Menon & Minchul Shin, 2020. "Probability Forecast Combination via Entropy Regularized Wasserstein Distance," Working Papers 20-31/R, Federal Reserve Bank of Philadelphia.
    15. 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.
    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. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Davide Pettenuzzo & Francesco Ravazzolo, 2016. "Optimal Portfolio Choice Under Decision‐Based Model Combinations," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(7), pages 1312-1332, November.
    3. Christian Kascha & Francesco Ravazzolo, 2010. "Combining inflation density forecasts," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 29(1-2), pages 231-250.
    4. Barbara Rossi, 2019. "Forecasting in the presence of instabilities: How do we know whether models predict well and how to improve them," Economics Working Papers 1711, Department of Economics and Business, Universitat Pompeu Fabra, revised Jul 2021.
    5. 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.
    6. Knut Are Aastveit & Francesco Ravazzolo & Herman K. van Dijk, 2018. "Combined Density Nowcasting in an Uncertain Economic Environment," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(1), pages 131-145, January.
    7. Clements, Michael P., 2018. "Are macroeconomic density forecasts informative?," International Journal of Forecasting, Elsevier, vol. 34(2), pages 181-198.
    8. Federico Bassetti & Roberto Casarin & Francesco Ravazzolo, 2019. "Density Forecasting," BEMPS - Bozen Economics & Management Paper Series BEMPS59, Faculty of Economics and Management at the Free University of Bozen.
    9. Knut Are Aastveit & Karsten R. Gerdrup & Anne Sofie Jore & Leif Anders Thorsrud, 2014. "Nowcasting GDP in Real Time: A Density Combination Approach," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(1), pages 48-68, January.
    10. Dr. James Mitchell, 2009. "Measuring Output Gap Uncertainty," National Institute of Economic and Social Research (NIESR) Discussion Papers 342, National Institute of Economic and Social Research.
    11. Garratt, Anthony & Mitchell, James & Vahey, Shaun P., 2014. "Measuring output gap nowcast uncertainty," International Journal of Forecasting, Elsevier, vol. 30(2), pages 268-279.
    12. Roberto Casarin & Giulia Mantoan & Francesco Ravazzolo, 2016. "Bayesian Calibration of Generalized Pools of Predictive Distributions," Econometrics, MDPI, vol. 4(1), pages 1-24, March.
    13. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    14. Gian Luigi Mazzi & James Mitchell & Gaetana Montana, 2014. "Density Nowcasts and Model Combination: Nowcasting Euro-Area GDP Growth over the 2008–09 Recession," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 76(2), pages 233-256, April.
    15. Hasumi, Ryo & Iiboshi, Hirokuni & Matsumae, Tatsuyoshi & Nakamura, Daisuke, 2019. "Does a financial accelerator improve forecasts during financial crises? Evidence from Japan with prediction-pooling methods," Journal of Asian Economics, Elsevier, vol. 60(C), pages 45-68.
    16. Wolden Bache, Ida & Sofie Jore, Anne & Mitchell, James & Vahey, Shaun P., 2011. "Combining VAR and DSGE forecast densities," Journal of Economic Dynamics and Control, Elsevier, vol. 35(10), pages 1659-1670, October.
    17. Shaun P Vahey & Elizabeth C Wakerly, 2013. "Moving towards probability forecasting," BIS Papers chapters, in: Bank for International Settlements (ed.), Globalisation and inflation dynamics in Asia and the Pacific, volume 70, pages 3-8, Bank for International Settlements.
    18. Hall, Stephen G. & Mitchell, James, 2007. "Combining density forecasts," International Journal of Forecasting, Elsevier, vol. 23(1), pages 1-13.
    19. 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.
    20. Ravazzolo Francesco & Vahey Shaun P., 2014. "Forecast densities for economic aggregates from disaggregate ensembles," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 18(4), pages 1-15, September.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bdi:wptemi:td_979_14. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/bdigvit.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.