Bayesian nonparametric change point detection for multivariate time series with missing observations

A time series is a commonly observed type of data, and it is analyzed in several ways in real applications. Within the possible analysis, change point detection is one of the crucial inferential targets for studying the behavior of a time series. We consider a multiple change point detection model for a multivariate time series. Among the possible approaches to perform multiple change point detection, we propose an extension to the multivariate case of one of the main state-of-the-art approaches, working in a Bayesian nonparametric framework. We combine a combinatorial prior distribution, which relies on a model-based clustering approach to detect the change points, with a multivariate kernel for time-dependent realizations in a general fashion. We further extend the model to the case of missing observations and derive opportune quantities to perform data imputation. Thereafter, we investigate the properties of the multivariate model with an extensive simulation study, and we apply the model to perform change point detection in two real data applications.