Detecting changes in time series: A product partition model with across-cluster correlation

• We present a new product partition model that includes dependence between clusters.
• A reversible jump MCMC algorithm is proposed to sample from the posterior distributions.
• We compare the partition model with across-cluster correlation to the standard model.
• The inclusion of correlation between clusters leads to a superior model.

The identification of multiple clusters and/or change points is a problem encountered in many subject areas, ranging from machine learning, pattern recognition, genetics, criminality and disease mapping to finance and industrial control. We present a product partition model that, for the first time, includes dependence between clusters or segments. The across-cluster dependence is introduced into the model through the prior distributions of the parameters. We adopt a reversible jump Markov chain Monte Carlo (MCMC) algorithm to sample from the posterior distributions. We compare the partition model with across-cluster correlation to two other models previously introduced in the literature, which includes the original product partition model (PPM). These models assume independence among the clusters. We illustrate the use of the proposed model with three case studies and we perform a Monte Carlo study. We show that the inclusion of correlation between clusters is a competitive model for change-point identification. By accounting for this correlation, we achieve substantial improvements in the parameter estimates.