Bayesian Analysis of Proportions via a Hidden Markov Model

Ceren Eda Can (), Gul Ergun () and Refik Soyer ()
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Ceren Eda Can: Hacettepe University
Gul Ergun: Hacettepe University
Refik Soyer: The George Washington University

Methodology and Computing in Applied Probability, 2022, vol. 24, issue 4, 3121-3139

Abstract: 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.

Keywords: Hidden Markov Model; Proportions; Beta distribution; Gibbs Sampling; Metropolis-Hastings algorithm; 62F15; 91B84; 60J10; 91B70; 62M05 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11009-022-09971-0

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