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Beta-Product Dependent Pitman-Yor Processes for Bayesian Inference

Author

Listed:
  • Federico Bassetti

    (Department of Mathematics, University of Pavia)

  • Roberto Casarin

    () (Department of Economics, University of Venice C� Foscari)

  • Fabrizio Leisen

    (Department of Statistics, Universidad Carlos III de Madrid)

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.

Suggested Citation

  • Federico Bassetti & Roberto Casarin & Fabrizio Leisen, 2013. "Beta-Product Dependent Pitman-Yor Processes for Bayesian Inference," Working Papers 2013:13, Department of Economics, University of Venice "Ca' Foscari".
  • Handle: RePEc:ven:wpaper:2013:13
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    8. 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.
    9. Roberto Casarin & Fausto Corradin & Francesco Ravazzolo & Nguyen Domenico Sartore & Wing-Keung Wong, 2020. "A Scoring Rule for Factor and Autoregressive Models Under Misspecification," Advances in Decision Sciences, Asia University, Taiwan, vol. 24(2), pages 66-103, June.
    10. Jin, Xin & Maheu, John M., 2016. "Bayesian semiparametric modeling of realized covariance matrices," Journal of Econometrics, Elsevier, vol. 192(1), pages 19-39.
    11. Florian Huber & Luca Rossini, 2020. "Inference in Bayesian Additive Vector Autoregressive Tree Models," Papers 2006.16333, arXiv.org.
    12. Roberto Casarin & Fausto Corradin & Francesco Ravazzolo & Nguyen Domenico Sartore & Wing-Keung Wong, 2020. "A Scoring Rule for Factor and Autoregressive Models Under Misspecification," Advances in Decision Sciences, Asia University, Taiwan, vol. 24(2), pages 66-103, June.
    13. 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".
    14. 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.
    15. 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.
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    18. Jim Griffin & Maria Kalli & Mark Steel, 2018. "Discussion of “Nonparametric Bayesian Inference in Applications”: Bayesian nonparametric methods in econometrics," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(2), pages 207-218, June.
    19. Peluso, Stefano & Mira, Antonietta & Muliere, Pietro, 2015. "Reinforced urn processes for credit risk models," Journal of Econometrics, Elsevier, vol. 184(1), pages 1-12.

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    More about this item

    Keywords

    Bayesian non�parametrics; Dirichlet process; Panel Time-series non�parametrics; Pitman-Yor process; Stick-breaking process; Vector autoregressive process; Repeated measurements non-parametrics;
    All these keywords.

    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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