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The Complexity of Forecast Testing

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  • Lance Fortnow
  • Rakesh V. Vohra

Abstract

Consider a weather forecaster predicting a probability of rain for the next day. We consider tests that, given a finite sequence of forecast predictions and outcomes, will either pass or fail the forecaster. Sandroni showed that any test which passes a forecaster who knows the distribution of nature can also be probabilistically passed by a forecaster with no knowledge of future events. We look at the computational complexity of such forecasters and exhibit a linear-time test and distribution of nature such that any forecaster without knowledge of the future who can fool the test must be able to solve computationally difficult problems. Thus, unlike Sandroni's work, a computationally efficient forecaster cannot always fool this test independently of nature. Copyright 2009 The Econometric Society.

Suggested Citation

  • Lance Fortnow & Rakesh V. Vohra, 2009. "The Complexity of Forecast Testing," Econometrica, Econometric Society, vol. 77(1), pages 93-105, January.
    • Handle: RePEc:ecm:emetrp:v:77:y:2009:i:1:p:93-105
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    Citations

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    Cited by:

    1. Dean Foster & Rakesh Vohra, 2011. "Calibration: Respice, Adspice, Prospice," Discussion Papers 1537, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. Griffiths, William E. & Newton, Lisa S. & O'Donnell, Christopher J., 2010. "Predictive densities for models with stochastic regressors and inequality constraints: Forecasting local-area wheat yield," International Journal of Forecasting, Elsevier, vol. 26(2), pages 397-412, April.
    3. Olszewski, Wojciech, 2015. "Calibration and Expert Testing," Handbook of Game Theory with Economic Applications,, Elsevier.
    4. Kavaler, Itay & Smorodinsky, Rann, 2019. "On comparison of experts," Games and Economic Behavior, Elsevier, vol. 118(C), pages 94-109.
    5. Ronen Gradwohl & Eran Shmaya, 2013. "Tractable Falsifiability," Discussion Papers 1564, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    6. Al-Najjar, Nabil I. & Sandroni, Alvaro & Smorodinsky, Rann & Weinstein, Jonathan, 2010. "Testing theories with learnable and predictive representations," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2203-2217, November.
    7. Marinovic, Iván & Ottaviani, Marco & Sorensen, Peter, 2013. "Forecasters’ Objectives and Strategies," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 690-720, Elsevier.
    8. Itay Kavaler & Rann Smorodinsky, 2019. "A Cardinal Comparison of Experts," Papers 1908.10649, arXiv.org, revised Feb 2020.
    9. , & ,, 2013. "Expressible inspections," Theoretical Economics, Econometric Society, vol. 8(2), May.

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