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Mixed hidden Markov models for longitudinal data: an overview. (English) Zbl 1238.62094

Summary: We review statistical methods which combine hidden Markov models (HMMs) and random effects models in a longitudinal setting, leading to the class of so-called mixed HMMs. This class of models has several interesting features. It deals with the dependence of a response variable on covariates, serial dependence, and unobserved heterogeneity in an HMM framework. It exploits the properties of HMMs, such as the relatively simple dependence structure and an efficient computational procedure, and allows one to handle a variety of real-world time-dependent data. We give details of the expectation-maximization algorithm for computing the maximum likelihood estimates of the model parameters and we illustrate the method with two real applications describing the relationship between patent counts and research and development expenditures, and between stock and market returns via the capital asset pricing model.

MSC:

62M05 Markov processes: estimation; hidden Markov models
62F10 Point estimation
62G05 Nonparametric estimation
91G70 Statistical methods; risk measures
65C60 Computational problems in statistics (MSC2010)
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