IDEAS home Printed from https://ideas.repec.org/p/cte/wsrepe/12160.html
   My bibliography  Save this paper

Beta-product Poisson-Dirichlet Processes

Author

Listed:
  • Bassetti, Federico
  • Casarin, Roberto
  • Leisen, Fabrizio

Abstract

Time series data may exhibit clustering over time and, in a multiple time series context, the clustering behavior may differ across the series. This paper is motivated by the Bayesian non--parametric modeling of the dependence between the clustering structures and the distributions of different time series. We follow a Dirichlet process mixture approach and introduce a new class of multivariate dependent Dirichlet processes (DDP). The proposed DDP are represented in terms of vector of stick-breaking processes with dependent weights. The weights are beta random vectors that determine different and dependent clustering effects along the dimension of the DDP vector. We discuss some theoretical properties and provide an efficient Monte Carlo Markov Chain algorithm for posterior computation. The effectiveness of the method is illustrated with a simulation study and an application to the United States and the European Union industrial production indexes.

Suggested Citation

  • Bassetti, Federico & Casarin, Roberto & Leisen, Fabrizio, 2011. "Beta-product Poisson-Dirichlet Processes," DES - Working Papers. Statistics and Econometrics. WS 12160, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:12160
    as

    Download full text from publisher

    File URL: https://e-archivo.uc3m.es/rest/api/core/bitstreams/c9c6cf8a-b357-488c-86f4-c79126ee6ad0/content
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Jensen, Mark J. & Maheu, John M., 2010. "Bayesian semiparametric stochastic volatility modeling," Journal of Econometrics, Elsevier, vol. 157(2), pages 306-316, August.
    3. Hatjispyros, Spyridon J. & Nicoleris, Theodoros & Walker, Stephen G., 2011. "Dependent mixtures of Dirichlet processes," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2011-2025, June.
    4. Leisen, Fabrizio & Lijoi, Antonio, 2011. "Vectors of two-parameter Poisson-Dirichlet processes," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 482-495, March.
    5. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    6. Jason A. Duan & Michele Guindani & Alan E. Gelfand, 2007. "Generalized Spatial Dirichlet Process Models," Biometrika, Biometrika Trust, vol. 94(4), pages 809-825.
    7. Rodríguez, Abel & Dunson, David B & Gelfand, Alan E, 2008. "The Nested Dirichlet Process," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 1131-1154.
    8. Griffin, J.E. & Steel, M.F.J., 2011. "Stick-breaking autoregressive processes," Journal of Econometrics, Elsevier, vol. 162(2), pages 383-396, June.
    9. Ishwaran H. & James L. F, 2001. "Gibbs Sampling Methods for Stick Breaking Priors," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 161-173, March.
    10. 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.
    11. 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, August.
    12. J. E. Griffin, 2011. "Inference in Infinite Superpositions of Non-Gaussian Ornstein--Uhlenbeck Processes Using Bayesian Nonparametic Methods," Journal of Financial Econometrics, Oxford University Press, vol. 9(3), pages 519-549, Summer.
    13. Teh, Yee Whye & Jordan, Michael I. & Beal, Matthew J. & Blei, David M., 2006. "Hierarchical Dirichlet Processes," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1566-1581, December.
    14. Michael P. Clements & Hans-Martin Krolzig, 1998. "A comparison of the forecast performance of Markov-switching and threshold autoregressive models of US GNP," Econometrics Journal, Royal Economic Society, vol. 1(Conferenc), pages 47-75.
    15. Yeonseung Chung & David Dunson, 2011. "The local Dirichlet process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(1), pages 59-80, February.
    16. Olkin, Ingram & Liu, Ruixue, 2003. "A bivariate beta distribution," Statistics & Probability Letters, Elsevier, vol. 62(4), pages 407-412, May.
    17. Michael L. Pennell & David B. Dunson, 2006. "Bayesian Semiparametric Dynamic Frailty Models for Multiple Event Time Data," Biometrics, The International Biometric Society, vol. 62(4), pages 1044-1052, December.
    18. Chang-Jin Kim & Christian J. Murray, 2002. "Permanent and transitory components of recessions," Empirical Economics, Springer, vol. 27(2), pages 163-183.
    19. Dunson, David B. & Xue, Ya & Carin, Lawrence, 2008. "The Matrix Stick-Breaking Process: Flexible Bayes Meta-Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 317-327, March.
    20. Sinae Kim & Mahlet G. Tadesse & Marina Vannucci, 2006. "Variable selection in clustering via Dirichlet process mixture models," Biometrika, Biometrika Trust, vol. 93(4), pages 877-893, December.
    21. Hans-Martin Krolzig, 2000. "Predicting Markov-Switching Vector Autoregressive Processes," Economics Series Working Papers 2000-W31, University of Oxford, Department of Economics.
    22. David B. Dunson & Shyamal D. Peddada, 2008. "Bayesian nonparametric inference on stochastic ordering," Biometrika, Biometrika Trust, vol. 95(4), pages 859-874.
    23. Rodríguez, Abel & Dunson, David B. & Gelfand, Alan E., 2010. "Latent Stick-Breaking Processes," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 647-659.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yong Song, 2014. "Modelling Regime Switching And Structural Breaks With An Infinite Hidden Markov Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(5), pages 825-842, August.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bassetti, Federico & Casarin, Roberto & Leisen, Fabrizio, 2014. "Beta-product dependent Pitman–Yor processes for Bayesian inference," Journal of Econometrics, Elsevier, vol. 180(1), pages 49-72.
    2. Billio, Monica & Casarin, Roberto & Rossini, Luca, 2019. "Bayesian nonparametric sparse VAR models," Journal of Econometrics, Elsevier, vol. 212(1), pages 97-115.
    3. Stefano Favaro & Antonio Lijoi & Igor Prünster, 2012. "On the stick–breaking representation of normalized inverse Gaussian priors," DEM Working Papers Series 008, University of Pavia, Department of Economics and Management.
    4. Jin, Xin & Maheu, John M., 2016. "Bayesian semiparametric modeling of realized covariance matrices," Journal of Econometrics, Elsevier, vol. 192(1), pages 19-39.
    5. Weixuan Zhu & Fabrizio Leisen, 2015. "A multivariate extension of a vector of two-parameter Poisson-Dirichlet processes," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(1), pages 89-105, March.
    6. Federico Bassetti & Roberto Casarin & Francesco Ravazzolo, 2018. "Bayesian Nonparametric Calibration and Combination of Predictive Distributions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 675-685, April.
    7. Yeonseung Chung & David Dunson, 2011. "The local Dirichlet process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(1), pages 59-80, February.
    8. Monica Billio & Roberto Casarin & Luca Rossini, 2016. "Bayesian nonparametric sparse seemingly unrelated regression model (SUR)," Working Papers 2016:20, Department of Economics, University of Venice "Ca' Foscari".
    9. Billio, Monica & Casarin, Roberto & Ravazzolo, Francesco & van Dijk, Herman K., 2012. "Combination schemes for turning point predictions," The Quarterly Review of Economics and Finance, Elsevier, vol. 52(4), pages 402-412.
    10. Michael L. Pennell & David B. Dunson, 2008. "Nonparametric Bayes Testing of Changes in a Response Distribution with an Ordinal Predictor," Biometrics, The International Biometric Society, vol. 64(2), pages 413-423, June.
    11. Monica Billio & Roberto Casarin & Francesco Ravazzolo & Herman K. van Dijk, 2013. "Interactions between Eurozone and US Booms and Busts: A Bayesian Panel Markov-switching VAR Model," Tinbergen Institute Discussion Papers 13-142/III, Tinbergen Institute, revised 01 Nov 2014.
    12. Bruno Scarpa & David B. Dunson, 2014. "Enriched Stick-Breaking Processes for Functional Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 647-660, June.
    13. Hatjispyros, Spyridon J. & Nicoleris, Theodoros & Walker, Stephen G., 2016. "Random density functions with common atoms and pairwise dependence," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 236-249.
    14. Martínez-Ovando Juan Carlos & Walker Stephen G., 2011. "Time-series Modelling, Stationarity and Bayesian Nonparametric Methods," Working Papers 2011-08, Banco de México.
    15. Shamsi Zamenjani, Azam, 2021. "Do financial variables help predict the conditional distribution of the market portfolio?," Journal of Empirical Finance, Elsevier, vol. 62(C), pages 327-345.
    16. Griffin, J.E. & Steel, M.F.J., 2011. "Stick-breaking autoregressive processes," Journal of Econometrics, Elsevier, vol. 162(2), pages 383-396, June.
    17. repec:jss:jstsof:40:i05 is not listed on IDEAS
    18. Knut Are Aastveit & Anne Sofie Jore & Francesco Ravazzolo, 2014. "Forecasting recessions in real time," Working Paper 2014/02, Norges Bank.
    19. Hatjispyros, Spyridon J. & Merkatas, Christos & Nicoleris, Theodoros & Walker, Stephen G., 2018. "Dependent mixtures of geometric weights priors," Computational Statistics & Data Analysis, Elsevier, vol. 119(C), pages 1-18.
    20. Leisen, Fabrizio & Lijoi, Antonio, 2011. "Vectors of two-parameter Poisson-Dirichlet processes," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 482-495, March.
    21. Igor Prünster & Matteo Ruggiero, 2011. "A Bayesian nonparametric approach to modeling market share dynamics," Carlo Alberto Notebooks 217, Collegio Carlo Alberto.

    More about this item

    Keywords

    Bayesian non--parametrics;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cte:wsrepe:12160. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Ana Poveda (email available below). General contact details of provider: http://portal.uc3m.es/portal/page/portal/dpto_estadistica .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.