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Bayesian Analysis of Proportions via a Hidden Markov Model

Author

Listed:
  • Ceren Eda Can

    (Hacettepe University)

  • Gul Ergun

    (Hacettepe University)

  • Refik Soyer

    (The George Washington University)

Abstract

Time series of proportions arise in many contexts. In this paper, we consider a hidden Markov model (HMM) to describe temporal dependence in such series. In so doing, we introduce a Beta-HMM and develop its Bayesian analysis using Markov Chain Monte Carlo Methods (MCMC). Our proposed model is based on a conjugate prior for beta likelihood which enables us develop Bayesian posterior and predictive computations in an efficient manner. We also address the problem of assessing dimension of the HMM using the marginal likelihood of the model which can be evaluated using posterior samples. Finally, we implement our model and the Bayesian methodology using weekly data on market shares.

Suggested Citation

  • Ceren Eda Can & Gul Ergun & Refik Soyer, 2022. "Bayesian Analysis of Proportions via a Hidden Markov Model," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 3121-3139, December.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:4:d:10.1007_s11009-022-09971-0
    DOI: 10.1007/s11009-022-09971-0
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    References listed on IDEAS

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    1. Pievatolo, Antonio & Ruggeri, Fabrizio & Soyer, Refik, 2012. "A Bayesian hidden Markov model for imperfect debugging," Reliability Engineering and System Safety, Elsevier, vol. 103(C), pages 11-21.
    2. Dean W. Wichern & Richard H. Jones, 1977. "Assessing the Impact of Market Disturbances Using Intervention Analysis," Management Science, INFORMS, vol. 24(3), pages 329-337, November.
    3. 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 357-384, March.
    4. Taddy, Matthew A., 2010. "Autoregressive Mixture Models for Dynamic Spatial Poisson Processes: Application to Tracking Intensity of Violent Crime," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1403-1417.
    5. Emanuele Taufer, 2007. "Modelling stylized features in default rates," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 23(1), pages 73-82, January.
    6. da-Silva, C.Q. & Migon, H.S. & Correia, L.T., 2011. "Dynamic Bayesian beta models," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2074-2089, June.
    7. Hahn, Eugene David, 2008. "Mixture densities for project management activity times: A robust approach to PERT," European Journal of Operational Research, Elsevier, vol. 188(2), pages 450-459, July.
    8. Silvia Ferrari & Francisco Cribari-Neto, 2004. "Beta Regression for Modelling Rates and Proportions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(7), pages 799-815.
    9. Figueroa-Zúñiga, Jorge I. & Arellano-Valle, Reinaldo B. & Ferrari, Silvia L.P., 2013. "Mixed beta regression: A Bayesian perspective," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 137-147.
    10. Dong, A.X.D. & Chan, J.S.K., 2013. "Bayesian analysis of loss reserving using dynamic models with generalized beta distribution," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 355-365.
    11. Edilberto Cepeda-Cuervo & Jorge Alberto Achcar & Liliana Garrido Lopera, 2014. "Bivariate beta regression models: joint modeling of the mean, dispersion and association parameters," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(3), pages 677-687, March.
    12. Phillip Li, 2018. "Efficient MCMC estimation of inflated beta regression models," Computational Statistics, Springer, vol. 33(1), pages 127-158, March.
    13. Cox, Christopher, 1996. "Nonlinear quasi-likelihood models: applications to continuous proportions," Computational Statistics & Data Analysis, Elsevier, vol. 21(4), pages 449-461, April.
    14. Cook, Douglas O. & Kieschnick, Robert & McCullough, B.D., 2008. "Regression analysis of proportions in finance with self selection," Journal of Empirical Finance, Elsevier, vol. 15(5), pages 860-867, December.
    15. Billio Monica & Casarin Roberto, 2011. "Beta Autoregressive Transition Markov-Switching Models for Business Cycle Analysis," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 15(4), pages 1-32, September.
    16. Papke, Leslie E & Wooldridge, Jeffrey M, 1996. "Econometric Methods for Fractional Response Variables with an Application to 401(K) Plan Participation Rates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(6), pages 619-632, Nov.-Dec..
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