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The reproducible properties of correct forecasts

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  • Alvaro Sandroni

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    Abstract

    Each period, one outcome out of finitely many possibilities is observed. Each period, a forecaster announces some probability for the future outcomes based on the available data. An outsider wants to know if the forecaster has some knowledge of the data generating process. Let a test be an arbitrary function from sequences of forecasts and outcomes to {0,1}. When the test returns a 0 the test is said to reject the forecasts based on the outcome sequence. When the test resturns a 1 the test is said to not reject the forecasts based on the outcome sequence. Consider any test that does not reject the truth, i.e. it does not reject when the announced forecasts are the conditional probabilities of the data generating process. Based on Fan’s (1953) Minimax theorem, I show that it is possible to produce forecasts that will not be rejected on any sequence of outcomes. Copyright Springer-Verlag 2003

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    Bibliographic Info

    Article provided by Springer in its journal International Journal of Games Theory.

    Volume (Year): 32 (2003)
    Issue (Month): 1 (December)
    Pages: 151-159

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    Handle: RePEc:spr:jogath:v:32:y:2003:i:1:p:151-159

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    Related research

    Keywords: Forecasting; Testing; Calibration; Minimax theorem;

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    Cited by:
    1. Hu, Tai Wei & Shmaya, Eran, 2013. "Expressible inspections," Theoretical Economics, Econometric Society, vol. 8(2), May.
    2. Wojciech Olszewski & Alvaro Sandroni, 2006. "Strategic Manipulation of Empirical Tests," Discussion Papers 1425, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. Wojciech Olszewski & Alvaro Sandroni, 2011. "Falsifiability," American Economic Review, American Economic Association, vol. 101(2), pages 788-818, April.
    4. Glen Weyl, 2009. "A Simple Theory of Scientific Learning," Levine's Working Paper Archive 814577000000000067, David K. Levine.
    5. Alvaro Sandroni & Wojciech Olszewski, 2008. "Falsifiability," PIER Working Paper Archive 08-016, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    6. Eddie Dekel & Yossi Feinberg, 2006. "A True Expert Knows which Question Should be Asked," Discussion Papers 1385, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    7. Colin Stewart, 2009. "Nonmanipulable Bayesian Testing," Working Papers tecipa-360, University of Toronto, Department of Economics.
    8. Alvaro Sandroni & Wojciech Olszewski, 2008. "Manipulability of Future-Independent Tests," PIER Working Paper Archive 08-014, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    9. 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.
    10. Wojciech Olszewski & Marcin Pęski, 2011. "The Principal-Agent Approach to Testing Experts," American Economic Journal: Microeconomics, American Economic Association, vol. 3(2), pages 89-113, May.
    11. Yossi Feinberg & Colin Stewart, 2008. "Testing Multiple Forecasters," Econometrica, Econometric Society, vol. 76(3), pages 561-582, 05.
    12. Al-Najjar, Nabil & Sandroni, Alvaro, 2013. "A difficulty in the testing of strategic experts," Mathematical Social Sciences, Elsevier, vol. 65(1), pages 5-9.
    13. Frank Schorfheide & Kenneth I. Wolpin, 2013. "To Hold Out or Not to Hold Out," PIER Working Paper Archive 13-059, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    14. Dean Foster & Rakesh Vohra, 2011. "Calibration: Respice, Adspice, Prospice," Discussion Papers 1537, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    15. Frank Schorfheide & Kenneth I. Wolpin, 2013. "To Hold Out or Not to Hold Out," NBER Working Papers 19565, National Bureau of Economic Research, Inc.
    16. Feinberg, Yossi & Lambert, Nicolas S., 2011. "Mostly Calibrated," Research Papers 2090, Stanford University, Graduate School of Business.

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