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Calibrated Forecasting and Merging

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  • Ehud Kalai

Abstract

Consider a general finite-state stochastic process governed by an unknown objective probability distribution. A forecaster, observing the system, assigns subjective probabilities to future states. The subjective forecast merges to the objective distribution if, with time, forecasted probabilities converge to the (unknown) correct probabilities. The forecast is calibrated if observed long-run empirical distributions coincide with their forecasted probabilities. This paper links the unobserved reliability of forecasts to their observed empirical performance by showing full equilvalents between notions of merging and calibration.

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Bibliographic Info

Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1144.

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

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Postal: Center for Mathematical Studies in Economics and Management Science, Northwestern University, 580 Jacobs Center, 2001 Sheridan Road, Evanston, IL 60208-2014
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Web page: http://www.kellogg.northwestern.edu/research/math/
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  1. Sergiu Hart & Andreu Mas-Colell, 1997. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Game Theory and Information 9703006, EconWPA, revised 24 Mar 1997.
  2. Dov Monderer & Dov Samet & Aner Sela, 2010. "Belief Affirming in Learning Processes," Levine's Working Paper Archive 420, David K. Levine.
  3. 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.
  4. Ehud Kalai & Ehud Lehrer, 1990. "Merging Economic Forecasts," Discussion Papers 1035, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  5. Kalai, Ehud & Lehrer, Ehud, 1994. "Weak and strong merging of opinions," Journal of Mathematical Economics, Elsevier, vol. 23(1), pages 73-86, January.
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