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On the Aggregation of Probability Assessments: Regularized Mixtures of Predictive Densities for Eurozone Inflation and Real Interest Rates

Author

Listed:
  • Francis X. Diebold
  • Minchul Shin
  • Boyuan Zhang

Abstract

We propose methods for constructing regularized mixtures of density forecasts. We explore a variety of objectives and regularization penalties, and we use them in a substantive exploration of Eurozone inflation and real interest rate density forecasts. All individual inflation forecasters (even the ex post best forecaster) are outperformed by our regularized mixtures. From the Great Recession onward, the optimal regularization tends to move density forecasts’ probability mass from the centers to the tails, correcting for overconfidence.

Suggested Citation

  • Francis X. Diebold & Minchul Shin & Boyuan Zhang, 2021. "On the Aggregation of Probability Assessments: Regularized Mixtures of Predictive Densities for Eurozone Inflation and Real Interest Rates," Working Papers 21-06, Federal Reserve Bank of Philadelphia.
    • Handle: RePEc:fip:fedpwp:89897
    DOI: 10.21799/frbp.wp.2021.06
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    Cited by:

    1. Tony Chernis & Niko Hauzenberger & Florian Huber & Gary Koop & James Mitchell, 2023. "Predictive Density Combination Using a Tree-Based Synthesis Function," Staff Working Papers 23-61, Bank of Canada.
    2. Francis X. Diebold & Aaron Mora & Minchul Shin, 2025. "On the Wisdom of Crowds (of Economists)," PIER Working Paper Archive 25-008, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    3. Mr. Tobias Adrian & Domenico Giannone & Matteo Luciani & Mike West, 2025. "Scenario Synthesis and Macroeconomic Risk," IMF Working Papers 2025/105, International Monetary Fund.
    4. Chen, Yi-Ting & Liu, Chu-An & Su, Jiun-Hua, 2025. "Bregman model averaging for forecast combination," Journal of Econometrics, Elsevier, vol. 251(C).
    5. Tony Chernis & Niko Hauzenberger & Haroon Mumtaz & Michael Pfarrhofer, 2025. "A Bayesian Gaussian Process Dynamic Factor Model," Papers 2509.04928, arXiv.org.
    6. Lambert, Thomas & Mishra, Prachi, 2021. "The Politics of the Paycheck Protection Program," CEPR Discussion Papers 16842, C.E.P.R. Discussion Papers.
    7. James W. Taylor & Chao Wang, 2025. "Combining a Large Pool of Forecasts of Value-at-Risk and Expected Shortfall," Papers 2508.16919, arXiv.org.
    8. 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.
    9. Ricardo P. Masini & Marcelo C. Medeiros & Eduardo F. Mendes, 2023. "Machine learning advances for time series forecasting," Journal of Economic Surveys, Wiley Blackwell, vol. 37(1), pages 76-111, February.
    10. Chernis Tony, 2024. "Combining Large Numbers of Density Predictions with Bayesian Predictive Synthesis," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 28(2), pages 293-317, April.
    11. Bańbura, Marta & Brenna, Federica & Paredes, Joan & Ravazzolo, Francesco, 2021. "Combining Bayesian VARs with survey density forecasts: does it pay off?," Working Paper Series 2543, European Central Bank.
    12. Garratt, Anthony & Henckel, Timo & Vahey, Shaun P., 2023. "Empirically-transformed linear opinion pools," International Journal of Forecasting, Elsevier, vol. 39(2), pages 736-753.
    13. Bernaciak, Dawid & Griffin, Jim E., 2024. "A loss discounting framework for model averaging and selection in time series models," International Journal of Forecasting, Elsevier, vol. 40(4), pages 1721-1733.
    14. Todd E. Clark & Gergely Ganics & Elmar Mertens, 2022. "What is the Predictive Value of SPF Point and Density Forecasts?," Working Papers 22-37, Federal Reserve Bank of Cleveland.

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    JEL classification:

    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs

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