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Beta-product dependent Pitman–Yor processes for Bayesian inference

Author

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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.

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  • 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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    11. 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.
    12. Marcellino, Massimiliano & Foroni, Claudia & Casarin, Roberto & Ravazzolo, Francesco, 2017. "Uncertainty Through the Lenses of A Mixed-Frequency Bayesian Panel Markov Switching Model," CEPR Discussion Papers 12339, C.E.P.R. Discussion Papers.
    13. 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.
    14. 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.
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    16. Mike Tsionas & Marwan Izzeldin & Lorenzo Trapani, 2019. "Bayesian estimation of large dimensional time varying VARs using copulas," Papers 1912.12527, arXiv.org.
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    18. Zhang, Junyi & Dassios, Angelos, 2023. "Truncated two-parameter Poisson-Dirichlet approximation for Pitman-Yor process hierarchical models," LSE Research Online Documents on Economics 120294, London School of Economics and Political Science, LSE Library.
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    More about this item

    Keywords

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