Hidden Markov Mixtures for Change Detection in Unevenly Spaced Time Series

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This work tackles sequential data change-point detection, a research area with various applications in different fields. It focuses on analyzing sequential data such that the distance between locations of consecutive observations is not fixed. The models developed here for change detection extend a Hidden Markov Mixture approach originally designed to handle irregular spacing to improve the identification of atypical values. These models consider the probability of Markov dependence explained by the distance between locations. Bayesian inference is carried out via Gibbs Sampling. Informative priors for the dependency structure are crucial to identify clusters. The models adapt these priors to enable change identification in a general setting. Two mixture models are formulated: one for mean changes and another for mean or variance changes. Post-processing strategies are suggested to categorize observations among the components to facilitate change identification by the mixtures. These strategies are based on maximum posterior probability and consider the uncertainty associated with classifications. Models and clustering performances are evaluated in simulation studies including a Monte Carlo scheme. The analysis also explores three real illustrations. Finally, the proposed approaches are compared to existing clustering and change detection methods available in the literature.