Beta-Product Dependent Pitman-Yor Processes for Bayesian Inference

33 Pages Posted: 9 Jul 2013  

Federico Bassetti

University of Pavia

Roberto Casarin

University Ca' Foscari of Venice - Department of Economics

Fabrizio Leisen

University of Kent, Canterbury

Date Written: July 1, 2013

Abstract

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

Bassetti, Federico and Casarin, Roberto and Leisen, Fabrizio, Beta-Product Dependent Pitman-Yor Processes for Bayesian Inference (July 1, 2013). University Ca' Foscari of Venice, Dept. of Economics Research Paper Series No. 13/WP/2013. Available at SSRN: https://ssrn.com/abstract=2290959 or http://dx.doi.org/10.2139/ssrn.2290959

Federico Bassetti

University of Pavia ( email )

Corso Strada Nuova, 65
27100 Pavia, 27100
Italy

Roberto Casarin (Contact Author)

University Ca' Foscari of Venice - Department of Economics ( email )

San Giobbe 873/b
Venice, 30121
Italy
+39 030.298.91.49 (Phone)
+39 030.298.88.37 (Fax)

HOME PAGE: http://venus.unive.it/r.casarin/

Fabrizio Leisen

University of Kent, Canterbury ( email )

Cornwallis Building
Canterbury, Kent CT2 7NF
United Kingdom

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