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Forecast Hedging and Calibration

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  • Dean P. Foster
  • Sergiu Hart

Abstract

Calibration means that forecasts and average realized frequencies are close. We develop the concept of forecast hedging, which consists of choosing the forecasts so as to guarantee that the expected track record can only improve. This yields all the calibration results by the same simple basic argument while differentiating between them by the forecast-hedging tools used: deterministic and fixed point based versus stochastic and minimax based. Additional contributions are an improved definition of continuous calibration, ensuing game dynamics that yield Nash equilibria in the long run, and a new calibrated forecasting procedure for binary events that is simpler than all known such procedures.

Suggested Citation

  • Dean P. Foster & Sergiu Hart, 2021. "Forecast Hedging and Calibration," Journal of Political Economy, University of Chicago Press, vol. 129(12), pages 3447-3490.
    • Handle: RePEc:ucp:jpolec:doi:10.1086/716559
    DOI: 10.1086/716559
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    References listed on IDEAS

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    1. Foster, Dean P. & Vohra, Rakesh, 1999. "Regret in the On-Line Decision Problem," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 7-35, October.
    2. Sergiu Hart & Andreu Mas-Colell, 2013. "Stochastic Uncoupled Dynamics And Nash Equilibrium," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 8, pages 165-189, World Scientific Publishing Co. Pte. Ltd..
    3. Fudenberg, Drew & Levine, David K., 1999. "An Easier Way to Calibrate," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 131-137, October.
    4. Sergiu Hart, 2013. "Nash Equilibrium And Dynamics," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 12, pages 289-293, World Scientific Publishing Co. Pte. Ltd..
    5. Foster, Dean P., 1999. "A Proof of Calibration via Blackwell's Approachability Theorem," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 73-78, October.
    6. Foster, Dean P. & Hart, Sergiu, 2018. "Smooth calibration, leaky forecasts, finite recall, and Nash dynamics," Games and Economic Behavior, Elsevier, vol. 109(C), pages 271-293.
    7. Sergiu Hart & Andreu Mas-Colell, 2013. "Uncoupled Dynamics Do Not Lead To Nash Equilibrium," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 7, pages 153-163, World Scientific Publishing Co. Pte. Ltd..
    8. Foster, Dean P. & Vohra, Rakesh V., 1997. "Calibrated Learning and Correlated Equilibrium," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 40-55, October.
    9. Eddie Dekel & Yossi Feinberg, 2006. "Non-Bayesian Testing of a Stochastic Prediction," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 73(4), pages 893-906.
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    Cited by:

    1. Foster, Dean & Hart, Sergiu, 2023. ""Calibeating": beating forecasters at their own game," Theoretical Economics, Econometric Society, vol. 18(4), November.
    2. Sergiu Hart, 2022. "Calibrated Forecasts: The Minimax Proof," Papers 2209.05863, arXiv.org, revised Feb 2023.
    3. Varun Gupta & Christopher Jung & Georgy Noarov & Mallesh M. Pai & Aaron Roth, 2021. "Online Multivalid Learning: Means, Moments, and Prediction Intervals," Papers 2101.01739, arXiv.org.

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