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Bayesian inference for Hidden Markov Model

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  • Rosella Castellano

    (University of Macerata)

  • Luisa Scaccia

    (University of Macerata)

Abstract

� Hidden Markov Models can be considered an extension of mixture models, allowing for dependent observations. In a hierarchical Bayesian framework, we show how Reversible Jump Markov Chain Monte Carlo techniques can be used to estimate the parameters of a model, as well as the number of regimes. We consider a mixture of normal distributions characterized by different means and variances under each regime, extending the model proposed by Robert et al. (2000), based on a mixture of zero mean normal distributions.

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Bibliographic Info

Paper provided by Macerata University, Department of Finance and Economic Sciences in its series Working Papers with number 43-2007.

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Date of creation: Oct 2007
Date of revision: Oct 2008
Handle: RePEc:mcr:wpdief:wpaper00043

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  1. Chib, Siddhartha, 1996. "Calculating posterior distributions and modal estimates in Markov mixture models," Journal of Econometrics, Elsevier, vol. 75(1), pages 79-97, November.
  2. Peter J. Green, 2001. "Modelling Heterogeneity With and Without the Dirichlet Process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 28(2), pages 355-375.
  3. Billio, M. & Monfort, A. & Robert, C. P., 1999. "Bayesian estimation of switching ARMA models," Journal of Econometrics, Elsevier, vol. 93(2), pages 229-255, December.
  4. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-84, March.
  5. Engel, Charles & Hamilton, James D, 1990. "Long Swings in the Dollar: Are They in the Data and Do Markets Know It?," American Economic Review, American Economic Association, vol. 80(4), pages 689-713, September.
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