Beta-Product Dependent Pitman-Yor Processes for Bayesian Inference
33 Pages Posted: 9 Jul 2013
Date Written: July 1, 2013
Multiple time series data may exhibit clustering over time and the clustering effect may change across different series. This paper is motivated by the Bayesian non–parametric modelling of the dependence between clustering effects in multiple time series analysis. We follow a Dirichlet process mixture approach and define a new class of multivariate dependent Pitman-Yor processes (DPY). The proposed DPY are represented in terms of a vector of stick-breaking processes which determines dependent clustering structures in the time series. We follow a hierarchical specification of the DPY base measure to accounts for various degrees of information pooling across the series. We discuss some theoretical properties of the DPY and use them to define Bayesian non–parametric repeated measurement and vector autoregressive models. We provide efficient Monte Carlo Markov Chain algorithms for posterior computation of the proposed models and illustrate the effectiveness of the method with a simulation study and an application to the United States and the European Union business cycles.
Keywords: Bayesian non–parametrics, Dirichlet process, Panel Time-series non–parametrics, Pitman-Yor process, Stick-breaking process, Vector autoregressive process, Repeated measurements non-parametrics
JEL Classification: C11, C14, C32
Suggested Citation: Suggested Citation