Mistura markoviana oculta: detecção de pontos de mudança em séries com espaçamento irregular

Abstract

This work addresses change-point detection problems in sequential data, a research area with various applications, such as genetics, finance, signal processing, among others. The focus lies in analyzing unevenly spaced time series, that is, when the distance between time instants or locations of consecutive observations is not fixed. The models developed here for change detection are extensions of a Hidden Markov Mixture model published in 2020, originally designed for identifying atypical observations, and carry its capability to handle irregular spacing. These models consider dependence (Markovian) or independence between observations based on the distances between locations. Bayesian inference is carried out through indirect sampling via Gibbs Sampling. Informative prior specifications for the dependency structure are crucial to identify clusters. The developed models adapt these prior distributions to enable change identification in a general problem setting. Two mixture models are formulated: one for changes in the mean and another for multiparametric changes in the mean or variance. Post-processing methods are suggested to categorize observations among the components in order to facilitate change identification by the proposed mixtures. These methods are based on maximum posterior probability and consider the uncertainty associated with classifications. The performance of the models and clustering methods is evaluated through Monte Carlo simulations, using artificially irregularly spaced series, as well as in real-world applications. The proposed approach is compared to existing methods in the literature for clustering and change detection.