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Stick-breaking autoregressive processes

  • Griffin, J.E.
  • Steel, M.F.J.

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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Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 162 (2011)
Issue (Month): 2 (June)
Pages: 383-396

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Handle: RePEc:eee:econom:v:162:y:2011:i:2:p:383-396
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  1. Keisuke Hirano, 2002. "Semiparametric Bayesian Inference in Autoregressive Panel Data Models," Econometrica, Econometric Society, vol. 70(2), pages 781-799, March.
  2. Roberto Zelli & Maria Grazia Pittau, 2006. "Empirical evidence of income dynamics across EU regions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(5), pages 605-628.
  3. Chib, Siddhartha & Hamilton, Barton H., 2002. "Semiparametric Bayes analysis of longitudinal data treatment models," Journal of Econometrics, Elsevier, vol. 110(1), pages 67-89, September.
  4. Geweke, John & Keane, Michael, 2007. "Smoothly mixing regressions," Journal of Econometrics, Elsevier, vol. 138(1), pages 252-290, May.
  5. Jim E. Griffin & Mark F.J. Steel, 2002. "Semiparametric Bayesian Inference for Stochastic Frontier Models," Econometrics 0209001, EconWPA, revised 18 Sep 2002.
  6. Mark J. Jensen & John M. Maheu, 2009. "Bayesian Semiparametric Stochastic Volatility Modeling," Working Paper Series 23_09, The Rimini Centre for Economic Analysis, revised Jan 2009.
  7. Lancelot F. James & Antonio Lijoi & Igor Prünster, 2009. "Posterior Analysis for Normalized Random Measures with Independent Increments," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(1), pages 76-97.
  8. De Iorio, Maria & Muller, Peter & Rosner, Gary L. & MacEachern, Steven N., 2004. "An ANOVA Model for Dependent Random Measures," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 205-215, January.
  9. Jacquier, Eric & Polson, Nicholas G. & Rossi, P.E.Peter E., 2004. "Bayesian analysis of stochastic volatility models with fat-tails and correlated errors," Journal of Econometrics, Elsevier, vol. 122(1), pages 185-212, September.
  10. Peter Müller & Fernando Quintana & Gary Rosner, 2004. "A method for combining inference across related nonparametric Bayesian models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(3), pages 735-749.
  11. David B. Dunson & Natesh Pillai & Ju-Hyun Park, 2007. "Bayesian density regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(2), pages 163-183.
  12. Griffin, J.E. & Steel, M.F.J., 2006. "Order-Based Dependent Dirichlet Processes," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 179-194, March.
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