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Hidden Markov and semi-Markov models for count time series
(2022-06-17) Chorianopoulos, Vasilis; Χωριανόπουλος, Βασίλης; Athens University of Economics and Business, Department of Statistics; Vrontos, Ioannis; Pavlopoulos, Charalampos; Besbeas, Panagiotis
Hidden Markov models (HMMs) are models in which the distributionthat generates an observation depends on the state of an underlying and unobserved Markov process. HMMs have been employed in a variety of areas, including signal processing, bioinformatics, environment and ecology, and are noted for their flexibility and computational efficiency. In an HMM’sbasic model formulation, the consecutive time points spent in each state, called the dwell time, follows a geometric distribution. This assumption is mathematically and computationally very convenient and allows for an efficient likelihood evaluation and inference, however in some applications may be too restrictive or inappropriate. Hidden semi-Markov models (HSMMs)generalize hidden Markov models by allowing the dwell time in each state to follow any distribution on the positive integers. This generalization comes at a cost, since the likelihood evaluation is not straightforward. For that reason, a strategy of fitting HSMMs by using an HMM to represent the HSMM of interest is shown. With this way, the whole HMM methodology becomes applicable to the more general class of HSMMs. The approach is illustrated using a real data set on yearly counts of major earthquakes in the world. A variety of standard discrete parametric distributions for the dwell times is examined, such as the shifted Poisson or negative binomial, and the relative performance of HMMs and HSMMs is investigated.