Advanced Search
MyIDEAS: Login to save this paper or follow this series

Beta-Product Dependent Pitman-Yor Processes for Bayesian Inference

Contents:

Author Info

  • Federico Bassetti

    (Department of Mathematics, University of Pavia)

  • Roberto Casarin

    ()
    (Department of Economics, University of Venice Cà Foscari)

  • Fabrizio Leisen

    (Department of Statistics, Universidad Carlos III de Madrid)

Registered author(s):

    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.

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL: http://www.unive.it/media/allegato/DIP/Economia/Working_papers/Working_papers_2013/WP_DSE_bassetti_casarin_leisen_13_13.pdf
    File Function: First version, 2013
    Download Restriction: no

    Bibliographic Info

    Paper provided by Department of Economics, University of Venice "Ca' Foscari" in its series Working Papers with number 2013:13.

    as in new window
    Length: 33 pages
    Date of creation: 2013
    Date of revision:
    Handle: RePEc:ven:wpaper:2013:13

    Contact details of provider:
    Postal: Cannaregio, S. Giobbe no 873 , 30121 Venezia
    Phone: +39-0412349621
    Fax: +39-0412349176
    Email:
    Web page: http://www.unive.it/dip.economia
    More information through EDIRC

    Related research

    Keywords: Bayesian non–parametrics; Dirichlet process; Panel Time-series non–parametrics; Pitman-Yor process; Stick-breaking process; Vector autoregressive process; Repeated measurements non-parametrics;

    Find related papers by JEL classification:

    This paper has been announced in the following NEP Reports:

    References

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
    as in new window
    1. Jensen, Mark J. & Maheu, John M., 2010. "Bayesian semiparametric stochastic volatility modeling," Journal of Econometrics, Elsevier, Elsevier, vol. 157(2), pages 306-316, August.
    2. Gerhard Bry & Charlotte Boschan, 1971. "Cyclical Analysis of Time Series: Selected Procedures and Computer Programs," NBER Books, National Bureau of Economic Research, Inc, National Bureau of Economic Research, Inc, number bry_71-1.
    3. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, Econometric Society, vol. 57(2), pages 357-84, March.
    4. Edoardo Otranto & Giampiero Gallo, 2002. "A Nonparametric Bayesian Approach To Detect The Number Of Regimes In Markov Switching Models," Econometric Reviews, Taylor & Francis Journals, Taylor & Francis Journals, vol. 21(4), pages 477-496.
    5. 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, Royal Economic Society, vol. 1(Conferenc), pages C47-C75.
    6. Min, Chung-ki & Zellner, Arnold, 1993. "Bayesian and non-Bayesian methods for combining models and forecasts with applications to forecasting international growth rates," Journal of Econometrics, Elsevier, Elsevier, vol. 56(1-2), pages 89-118, March.
    7. Chang-Jin Kim & Christian J. Murray, 2002. "Permanent and transitory components of recessions," Empirical Economics, Springer, Springer, vol. 27(2), pages 163-183.
    8. 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, Elsevier, vol. 52(4), pages 402-412.
    9. 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, American Statistical Association, vol. 99, pages 205-215, January.
    10. Chib, Siddhartha & Greenberg, Edward, 1995. "Hierarchical analysis of SUR models with extensions to correlated serial errors and time-varying parameter models," Journal of Econometrics, Elsevier, Elsevier, vol. 68(2), pages 339-360, August.
    11. Nieto-Barajas, Luis E. & Walker, Stephen G., 2007. "Gibbs and autoregressive Markov processes," Statistics & Probability Letters, Elsevier, Elsevier, vol. 77(14), pages 1479-1485, August.
    12. Taddy, Matthew A., 2010. "Autoregressive Mixture Models for Dynamic Spatial Poisson Processes: Application to Tracking Intensity of Violent Crime," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 105(492), pages 1403-1417.
    13. Griffin, J.E. & Steel, M.F.J., 2006. "Order-Based Dependent Dirichlet Processes," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 101, pages 179-194, March.
    14. Litterman, Robert B, 1986. "Forecasting with Bayesian Vector Autoregressions-Five Years of Experience," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 4(1), pages 25-38, January.
    15. Leisen, Fabrizio & Lijoi, Antonio, 2011. "Vectors of two-parameter Poisson-Dirichlet processes," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 102(3), pages 482-495, March.
    16. Geweke, John & Amisano, Gianni, 2008. "Comparing and evaluating Bayesian predictive distributions of assets returns," Working Paper Series, European Central Bank 0969, European Central Bank.
    17. 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, Royal Statistical Society, vol. 66(3), pages 735-749.
    18. Sinae Kim & Mahlet G. Tadesse & Marina Vannucci, 2006. "Variable selection in clustering via Dirichlet process mixture models," Biometrika, Biometrika Trust, Biometrika Trust, vol. 93(4), pages 877-893, December.
    19. Christopher A. Sims & Tao Zha, 1996. "Bayesian methods for dynamic multivariate models," Working Paper, Federal Reserve Bank of Atlanta 96-13, Federal Reserve Bank of Atlanta.
    20. Gerhard Bry & Charlotte Boschan, 1971. "Foreword to "Cyclical Analysis of Time Series: Selected Procedures and Computer Programs"," NBER Chapters, National Bureau of Economic Research, Inc, in: Cyclical Analysis of Time Series: Selected Procedures and Computer Programs, pages -1 National Bureau of Economic Research, Inc.
    21. J. E. Griffin, 2011. "Inference in Infinite Superpositions of Non-Gaussian Ornstein--Uhlenbeck Processes Using Bayesian Nonparametic Methods," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 9(3), pages 519-549, Summer.
    22. 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, American Statistical Association, vol. 101, pages 1566-1581, December.
    23. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, Econometric Society, vol. 48(1), pages 1-48, January.
    24. Yeonseung Chung & David Dunson, 2011. "The local Dirichlet process," Annals of the Institute of Statistical Mathematics, Springer, Springer, vol. 63(1), pages 59-80, February.
    25. Griffin, J.E. & Steel, M.F.J., 2011. "Stick-breaking autoregressive processes," Journal of Econometrics, Elsevier, Elsevier, vol. 162(2), pages 383-396, June.
    26. Olkin, Ingram & Liu, Ruixue, 2003. "A bivariate beta distribution," Statistics & Probability Letters, Elsevier, Elsevier, vol. 62(4), pages 407-412, May.
    27. Rodríguez, Abel & Dunson, David B. & Gelfand, Alan E., 2010. "Latent Stick-Breaking Processes," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 105(490), pages 647-659.
    28. Lorenzo Trippa & Peter Müller & Wesley Johnson, 2011. "The multivariate beta process and an extension of the Polya tree model," Biometrika, Biometrika Trust, Biometrika Trust, vol. 98(1), pages 17-34.
    29. Rodríguez, Abel & Dunson, David B & Gelfand, Alan E, 2008. "The Nested Dirichlet Process," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 103(483), pages 1131-1154.
    Full references (including those not matched with items on IDEAS)

    Citations

    Lists

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    Statistics

    Access and download statistics

    Corrections

    When requesting a correction, please mention this item's handle: RePEc:ven:wpaper:2013:13. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Geraldine Ludbrook).

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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