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Mixed Density based Copula Likelihood

Author

Listed:
  • Kazim Azam

    (VU University Amsterdam, the Netherlands)

  • Andre Lucas

    (VU University Amsterdam, the Netherlands)

Abstract

We consider a new copula method for mixed marginals of discrete and continuous random variables. Unlike the Bayesian methods in the literature, we use maximum likelihood estimation based on closed-form copula functions. We show with a simulation that our methodology performs similar to the method of Hoff (2007) for mixed data, but is considerably simpler to estimate. We extend to a time series setting, where the parameters are allowed to vary over time. In an empirical application using data from the 2013 Household Finance Survey, we show how the copula dependence between income (continuous) and discrete household characteristics varies across groups who were affected differently by the recent economic crisis.

Suggested Citation

  • Kazim Azam & Andre Lucas, 2015. "Mixed Density based Copula Likelihood," Tinbergen Institute Discussion Papers 15-003/IV/DSF084, Tinbergen Institute.
  • Handle: RePEc:tin:wpaper:20150003
    as

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    File URL: https://papers.tinbergen.nl/15003.pdf
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    References listed on IDEAS

    as
    1. Creal, Drew & Koopman, Siem Jan & Lucas, André, 2011. "A Dynamic Multivariate Heavy-Tailed Model for Time-Varying Volatilities and Correlations," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(4), pages 552-563.
    2. Andrew Harvey & Alessandra Luati, 2014. "Filtering With Heavy Tails," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1112-1122, September.
    3. Murat K. Munkin & Pravin K. Trivedi, 1999. "Simulated maximum likelihood estimation of multivariate mixed-Poisson regression models, with application," Econometrics Journal, Royal Economic Society, vol. 2(1), pages 29-48.
    4. André Lucas & Bernd Schwaab & Xin Zhang, 2014. "Conditional Euro Area Sovereign Default Risk," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(2), pages 271-284, April.
    5. Michael Pitt & David Chan & Robert Kohn, 2006. "Efficient Bayesian inference for Gaussian copula regression models," Biometrika, Biometrika Trust, vol. 93(3), pages 537-554, September.
    6. Genest, Christian & Nešlehová, Johanna, 2007. "A Primer on Copulas for Count Data," ASTIN Bulletin, Cambridge University Press, vol. 37(2), pages 475-515, November.
    7. Michael S. Smith & Mohamad A. Khaled, 2012. "Estimation of Copula Models With Discrete Margins via Bayesian Data Augmentation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 290-303, March.
    8. Andrew J. Patton, 2006. "Modelling Asymmetric Exchange Rate Dependence," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(2), pages 527-556, May.
    9. Drew Creal & Siem Jan Koopman & André Lucas, 2013. "Generalized Autoregressive Score Models With Applications," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(5), pages 777-795, August.
    10. Rodriguez, Juan Carlos, 2007. "Measuring financial contagion: A Copula approach," Journal of Empirical Finance, Elsevier, vol. 14(3), pages 401-423, June.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    copula; discrete data; time series;

    JEL classification:

    • 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
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions

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