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An Asymptotic Theory of Bayesian Inference for Time Series


  • Phillips, Peter C B
  • Ploberger, Werner


A limiting representation of the Bayesian data density is obtained and shown to be the same general exponential form for a wide class of likelihoods and prior distributions. An embedding theorem is given which shows how to embed the exponential density in a continuous time process. From the embedding, the authors obtain a large sample approximation to the model of the data that corresponds to the exponential density. This has the form of discrete observations drawn from a nonlinear stochastic differential equation driven by Brownian motion. No assumptions concerning stationarity or rates of convergence are required in the asymptotics. Some implications for statistical testing are explored. Copyright 1996 by The Econometric Society.

Suggested Citation

  • Phillips, Peter C B & Ploberger, Werner, 1996. "An Asymptotic Theory of Bayesian Inference for Time Series," Econometrica, Econometric Society, vol. 64(2), pages 381-412, March.
  • Handle: RePEc:ecm:emetrp:v:64:y:1996:i:2:p:381-412

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    References listed on IDEAS

    1. Leslie M. Marx & Steven A. Matthews, 2000. "Dynamic Voluntary Contribution to a Public Project," Review of Economic Studies, Oxford University Press, vol. 67(2), pages 327-358.
    2. Bergemann, Dirk & Hege, Ulrich, 1998. "Venture capital financing, moral hazard, and learning," Journal of Banking & Finance, Elsevier, vol. 22(6-8), pages 703-735, August.
    3. Ben Lockwood & Jonathan P. Thomas, 2002. "Gradualism and Irreversibility," Review of Economic Studies, Oxford University Press, vol. 69(2), pages 339-356.
    4. Harris, C., 1993. "Generalized Solutions of Stochastic Differential Games in One Dimension," Papers 44, Boston University - Industry Studies Programme.
    5. Dirk Bergemann & Ulrigh Hege, 2005. "The Financing of Innovation: Learning and Stopping," RAND Journal of Economics, The RAND Corporation, vol. 36(4), pages 719-752, Winter.
    6. Patrick Bolton & Christopher Harris, 1999. "Strategic Experimentation," Econometrica, Econometric Society, vol. 67(2), pages 349-374, March.
    7. Rothschild, Michael, 1974. "A two-armed bandit theory of market pricing," Journal of Economic Theory, Elsevier, vol. 9(2), pages 185-202, October.
    8. Anat R. Admati & Motty Perry, 1991. "Joint Projects without Commitment," Review of Economic Studies, Oxford University Press, vol. 58(2), pages 259-276.
    9. Keller, Godfrey & Rady, Sven, 2003. " Price Dispersion and Learning in a Dynamic Differentiated-Goods Duopoly," RAND Journal of Economics, The RAND Corporation, vol. 34(1), pages 138-165, Spring.
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