IDEAS home Printed from https://ideas.repec.org/p/fip/fedpwp/88545.html
   My bibliography  Save this paper

Probability Forecast Combination via Entropy Regularized Wasserstein Distance

Author

Listed:
  • Ryan Cumings-Menon
  • Minchul Shin

Abstract

We propose probability and density forecast combination methods that are defined using the entropy regularized Wasserstein distance. First, we provide a theoretical characterization of the combined density forecast based on the regularized Wasserstein distance under the Gaus-sian assumption. Second, we show how this type of regularization can improve the predictive power of the resulting combined density. Third, we provide a method for choosing the tuning parameter that governs the strength of regularization. Lastly, we apply our proposed method to the U.S. inflation rate density forecasting, and illustrate how the entropy regularization can improve the quality of predictive density relative to its unregularized counterpart.

Suggested Citation

  • Ryan Cumings-Menon & Minchul Shin, 2020. "Probability Forecast Combination via Entropy Regularized Wasserstein Distance," Working Papers 20-31/R, Federal Reserve Bank of Philadelphia.
  • Handle: RePEc:fip:fedpwp:88545
    DOI: 10.21799/frbp.wp.2020.31
    as

    Download full text from publisher

    File URL: https://philadelphiafed.org/-/media/research-and-data/publications/working-papers/2020/wp20-31r.pdf
    Download Restriction: no

    File URL: https://libkey.io/10.21799/frbp.wp.2020.31?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Michael W. McCracken & Serena Ng, 2021. "FRED-QD: A Quarterly Database for Macroeconomic Research," Review, Federal Reserve Bank of St. Louis, vol. 103(1), pages 1-44, January.
    2. Fabio Busetti, 2017. "Quantile Aggregation of Density Forecasts," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 79(4), pages 495-512, August.
    3. Geweke, John & Amisano, Gianni, 2011. "Optimal prediction pools," Journal of Econometrics, Elsevier, vol. 164(1), pages 130-141, September.
    4. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    5. G. Elliott & C. Granger & A. Timmermann (ed.), 2006. "Handbook of Economic Forecasting," Handbook of Economic Forecasting, Elsevier, edition 1, volume 1, number 1.
    6. 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.
    7. Diebold, Francis X. & Shin, Minchul, 2019. "Machine learning for regularized survey forecast combination: Partially-egalitarian LASSO and its derivatives," International Journal of Forecasting, Elsevier, vol. 35(4), pages 1679-1691.
    8. Clemen, Robert T., 1989. "Combining forecasts: A review and annotated bibliography," International Journal of Forecasting, Elsevier, vol. 5(4), pages 559-583.
    9. 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.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Li, Li & Kang, Yanfei & Li, Feng, 2023. "Bayesian forecast combination using time-varying features," International Journal of Forecasting, Elsevier, vol. 39(3), pages 1287-1302.
    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. 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.
    8. 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).
    9. Gergely Akos Ganics, 2017. "Optimal density forecast combinations," Working Papers 1751, Banco de España.
    10. Fabio Busetti, 2017. "Quantile Aggregation of Density Forecasts," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 79(4), pages 495-512, August.
    11. Miranda-Agrippino, Silvia & Ricco, Giovanni, 2018. "Bayesian Vector Autoregressions," The Warwick Economics Research Paper Series (TWERPS) 1159, University of Warwick, Department of Economics.
    12. Fabio Canova & Christian Matthes, 2021. "Dealing with misspecification in structural macroeconometric models," Quantitative Economics, Econometric Society, vol. 12(2), pages 313-350, May.
    13. repec:bny:wpaper:0003 is not listed on IDEAS
    14. Conflitti, Cristina & De Mol, Christine & Giannone, Domenico, 2015. "Optimal combination of survey forecasts," International Journal of Forecasting, Elsevier, vol. 31(4), pages 1096-1103.
    15. Tae-Hwy Lee & Ekaterina Seregina, 2020. "Learning from Forecast Errors: A New Approach to Forecast Combination," Working Papers 202024, University of California at Riverside, Department of Economics.
    16. repec:bny:wpaper:0073 is not listed on IDEAS
    17. Garratt, Anthony & Henckel, Timo & Vahey, Shaun P., 2023. "Empirically-transformed linear opinion pools," International Journal of Forecasting, Elsevier, vol. 39(2), pages 736-753.
    18. 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.
    19. Yusupova, Alisa & Pavlidis, Nicos G. & Pavlidis, Efthymios G., 2023. "Dynamic linear models with adaptive discounting," International Journal of Forecasting, Elsevier, vol. 39(4), pages 1925-1944.
    20. repec:bny:wpaper:0029 is not listed on IDEAS
    21. Laurent L. Pauwels & Andrey L. Vasnev, 2017. "Forecast combination for discrete choice models: predicting FOMC monetary policy decisions," Empirical Economics, Springer, vol. 52(1), pages 229-254, February.
    22. Čapek, Jan & Crespo Cuaresma, Jesús & Hauzenberger, Niko & Reichel, Vlastimil, 2023. "Macroeconomic forecasting in the euro area using predictive combinations of DSGE models," International Journal of Forecasting, Elsevier, vol. 39(4), pages 1820-1838.
    23. Tony Chernis & Taylor Webley, 2022. "Nowcasting Canadian GDP with Density Combinations," Discussion Papers 2022-12, Bank of Canada.

    More about this item

    Keywords

    Entropy regularization; Wasserstein distance; optimal transport; density forecasting; model combination;
    All these keywords.

    JEL classification:

    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - 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:fip:fedpwp:88545. 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: Beth Paul (email available below). General contact details of provider: https://edirc.repec.org/data/frbphus.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.