Stick-breaking autoregressive processes |
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Authors: | JE Griffin MFJ Steel |
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Institution: | a School of Mathematics, Statistics and Actuarial Science, University of Kent, UK;b Department of Statistics, University of Warwick, UK |
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Abstract: | 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. |
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Keywords: | Bayesian nonparametrics Dirichlet process Poisson– Dirichlet process Time-dependent nonparametrics |
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