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.

时间序列的比例出现在许多情况下。在本文中，我们考虑使用隐马尔可夫模型 (HMM) 来描述此类序列中的时间依赖性。在此过程中，我们引入了 Beta-HMM 并使用马尔可夫链蒙特卡罗方法 (MCMC) 开发其贝叶斯分析。我们提出的模型基于 beta 似然的共轭先验，这使我们能够以有效的方式开发贝叶斯后验和预测计算。我们还解决了使用可以使用后验样本评估的模型的边际似然来评估 HMM 维度的问题。最后，我们使用每周市场份额数据来实施我们的模型和贝叶斯方法。