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Beta-product dependent Pitman–Yor processes for Bayesian inference

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

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 vectors of stick-breaking processes which determine dependent clustering structures in the time series. We follow a hierarchical specification of the DPY base measure to account 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 cycle.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:econom:v:180:y:2014:i:1:p:49-72
    DOI: 10.1016/j.jeconom.2014.01.007
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    Cited by:

    1. Fisher, Mark & Jensen, Mark J., 2019. "Bayesian inference and prediction of a multiple-change-point panel model with nonparametric priors," Journal of Econometrics, Elsevier, vol. 210(1), pages 187-202.
    2. repec:bla:jorssb:v:79:y:2017:i:2:p:525-545 is not listed on IDEAS
    3. repec:eee:econom:v:212:y:2019:i:1:p:97-115 is not listed on IDEAS
    4. repec:eee:ecolet:v:176:y:2019:i:c:p:55-59 is not listed on IDEAS
    5. Jin, Xin & Maheu, John M., 2016. "Bayesian semiparametric modeling of realized covariance matrices," Journal of Econometrics, Elsevier, vol. 192(1), pages 19-39.
    6. Federico Bassetti & Roberto Casarin & Francesco Ravazzolo, 2015. "Bayesian nonparametric calibration and combination of predictive distributions," Working Paper 2015/03, Norges Bank.
    7. Roberto Casarin & Claudia Foroni & Massimiliano Marcellino & Francesco Ravazzolo, 2016. "Uncertainty Through the Lenses of A Mixed-Frequency Bayesian Panel Markov Switching Model," Working Papers 585, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    8. Maria Kokoreva & Anastasia Stepanova, 2013. "Financial architecture and corporate performance: evidence from Russia," HSE Working papers WP BRP 21/FE/2013, National Research University Higher School of Economics.
    9. Luis E. Nieto-Barajas & Fernando A. Quintana, 2016. "A Bayesian Non-Parametric Dynamic AR Model for Multiple Time Series Analysis," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(5), pages 675-689, September.
    10. Roberto Casarin & Stefano Grassi & Francesco Ravazzolo & Herman K. van Dijk, 2015. "Dynamic predictive density combinations for large data sets in economics and finance," Working Paper 2015/12, Norges Bank.
    11. Roberto Casarin & Fausto Corradin & Francesco Ravazzolo & Domenico Sartore, 2018. "A scoring rule for factor and autoregressive models under misspecification," Working Papers 2018:18, Department of Economics, University of Venice "Ca' Foscari".
    12. 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".
    13. Billio, Monica & Casarin, Roberto & Rossini, Luca, 2019. "Bayesian nonparametric sparse VAR models," Journal of Econometrics, Elsevier, vol. 212(1), pages 97-115.
    14. 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.
    15. repec:taf:jnlbes:v:36:y:2018:i:1:p:101-114 is not listed on IDEAS
    16. repec:spr:stmapp:v:27:y:2018:i:2:d:10.1007_s10260-017-0384-0 is not listed on IDEAS
    17. Peluso, Stefano & Mira, Antonietta & Muliere, Pietro, 2015. "Reinforced urn processes for credit risk models," Journal of Econometrics, Elsevier, vol. 184(1), pages 1-12.

    More about this item

    Keywords

    Bayesian non-parametrics; Dirichlet process; Panel vector autoregressive process; Pitman–Yor process; Stick-breaking process;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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