A Bayesian Nonparametric Approach for Time Series Clustering

In this work we propose a model-based clustering method for time series. The model uses an almost surely discrete Bayesian nonparametric prior to induce clustering of the series. Specifically we propose a general Poisson-Dirichlet process mixture model, which includes the Dirichlet process mixture model as a particular case. The model accounts for typical features present in a time series like trends, seasonal and temporal components. All or only part of these features can be used for clustering according to the user. Posterior inference is obtained via an easy to implement Markov chain Monte Carlo (MCMC) scheme. The best cluster is chosen according to a heterogeneity measure as well as the model selection criterion LPML (logarithm of the pseudo marginal likelihood). We illustrate our approach with a dataset of time series of share prices in the Mexican stock exchange.