Stick-breaking autoregressive processes

• Published in: Journal of econometrics Vol. 162; no. 2; pp. 383 - 396
• Main Authors: Griffin, J.E., Steel, M.F.J.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.06.2011; Elsevier; Elsevier Sequoia S.A
• Series: Journal of Econometrics
• Subjects: Bayesian analysis; Bayesian method; Bayesian nonparametrics; Bayesian nonparametrics Dirichlet process Poisson-Dirichlet process Time-dependent nonparametrics; Dirichlet process; Econometric models; Econometrics; Financial analysis; GDP; Gross Domestic Product; Markov analysis; Monte Carlo simulation; Poisson–Dirichlet process; Regression analysis; Statistical inference; Stick-breaking process; Studies; Time series; Time-dependent nonparametrics; Volatility; Bayesian nonparametrics; C11; C22; C14; Dirichlet process; Time-dependent nonparametrics; Poisson–Dirichlet process
• ISSN: 0304-4076; 1872-6895
• DOI: 10.1016/j.jeconom.2011.03.001

This paper considers the problem of defining a time-dependent nonparametric prior for use in Bayesian nonparametric modelling of time series. A recursive construction allows the definition of priors whose marginals have a general stick-breaking form. The processes with Poisson–Dirichlet and Dirichlet process marginals are investigated in some detail. We develop a general conditional Markov Chain Monte Carlo (MCMC) method for inference in the wide subclass of these models where the parameters of the marginal stick-breaking process are nondecreasing sequences. We derive a generalised Pólya urn scheme type representation of the Dirichlet process construction, which allows us to develop a marginal MCMC method for this case. We apply the proposed methods to financial data to develop a semi-parametric stochastic volatility model with a time-varying nonparametric returns distribution. Finally, we present two examples concerning the analysis of regional GDP and its growth.