Beta-Product Poisson-Dirichlet Processes

TL;DR

This paper introduces a novel multivariate dependent Dirichlet process model using beta-product stick-breaking processes to capture complex clustering dependencies across multiple time series.

Contribution

It proposes a new class of dependent Dirichlet processes with beta-product weights, enabling flexible modeling of dependent clustering structures in multivariate time series.

Findings

Effective in capturing diverse clustering patterns

Demonstrated through simulation studies

Applied successfully to industrial production indexes

Abstract

Time series data may exhibit clustering over time and, in a multiple time series context, the clustering behavior may differ across the series. This paper is motivated by the Bayesian non--parametric modeling of the dependence between the clustering structures and the distributions of different time series. We follow a Dirichlet process mixture approach and introduce a new class of multivariate dependent Dirichlet processes (DDP). The proposed DDP are represented in terms of vector of stick-breaking processes with dependent weights. The weights are beta random vectors that determine different and dependent clustering effects along the dimension of the DDP vector. We discuss some theoretical properties and provide an efficient Monte Carlo Markov Chain algorithm for posterior computation. The effectiveness of the method is illustrated with a simulation study and an application to the United States and the European Union industrial production indexes.