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Calibrated Forecasting and Merging

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Author Info
Ehud Kalai

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Abstract

Consider a general finite-state stochastic process governed by an unknown objective probability distribution. Observing the system, a forecaster assigns subjective probabilities to future states. The resulting subjective forecast merges to the objective distribution if, with time, the forecasted probabilities converge to the correct (but unknown) probabilities. The forecast is calibrated if observed long-run empirical distributions coincide with the forecasted probabilities. This paper links the unobserved reliability of forecasts to their observed empirical performance by demonstrating full equilvalence between notions of merging and of calibration. It also indicates some implications of this equilvalence for the literatures of forecasting and learning.

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File URL: http://www.kellogg.northwestern.edu/research/math/papers/1144.pdf
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Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1144R.

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Date of creation: Dec 1995
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Handle: RePEc:nwu:cmsems:1144r

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  1. Drew Fudenberg & David K. Levine, 1996. "An Easier Way to Calibrate," Levine's Working Paper Archive 2059, UCLA Department of Economics. [Downloadable!]
    Other versions:
  2. 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. [Downloadable!]
    Other versions:
  3. Alvaro Sandroni & Wojciech Olszewski, 2008. "Falsifiability," PIER Working Paper Archive 08-016, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania. [Downloadable!]
  4. Dean P. Foster & Rakesh V. Vohra, 1999. "Calibration, Expected Utility and Local Optimality," Discussion Papers 1254, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
  5. Eddie Dekel & Yossi Feinberg, 2005. "No Manipulation Results for Non-Bayesian Tests," Levine's Working Paper Archive 784828000000000217, UCLA Department of Economics. [Downloadable!]
  6. Eddie Dekel & Yossi Feinberg, 2006. "Non-Bayesian Testing of a Stochastic Prediction," Discussion Papers 1418, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
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  7. Nabil I. Al-Najjar & Jonathan Weinstein, 2006. "Comparative Testing of Experts," Levine's Working Paper Archive 321307000000000590, UCLA Department of Economics. [Downloadable!]
  8. Alvaro Sandroni & Wojciech Olszewski, 2008. "Strategic Manipulation of Empirical Tests," PIER Working Paper Archive 08-015, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania. [Downloadable!]
  9. Wojciech Olszewski & Alvaro Sandroni, 2006. "Strategic Manipulation of Empirical Tests," Discussion Papers 1425, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
  10. Feinberg, Yossi & Stewart, Colin, 2007. "Testing Multiple Forecasters," Research Papers 1957, Stanford University, Graduate School of Business. [Downloadable!]
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