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Mixed Data Kernel Copulas

Listed author(s):
  • Jeffrey S. Racine

    ()

    (McMaster University, Canada)

A number of approaches towards the kernel estimation of copula have appeared in the literature. Most existing approaches use a manifestation of the copula that requires kernel density estimation of bounded variates lying on a d-dimensional unit hypercube. This gives rise to a number of issues as it requires special treatment of the boundary and possible modifications to bandwidth selection routines, among others. Furthermore, existing kernel-based approaches are restricted to continuous date types only, though there is a growing interest in copula estimation with discrete marginals (see e.g. Smith & Khaled (2012) for a Bayesian approach). We demonstrate that using a simple inversion method (cf Nelsen (2006), Fermanian & Scaillet (2003)) can sidestep boundary issues while admitting mixed data types directly thereby extending the reach of kernel copula estimators. Bandwidth selection proceeds by the recently proposed method of Li & Racine (2013). Furthermore, there is no curse-of-dimensionality for the kernel-based copula estimator (though there is for the copula density estimator, as is the case for existing kernel copula density methods).

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File URL: http://www.rcfea.org/RePEc/pdf/wp46_13.pdf
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Paper provided by The Rimini Centre for Economic Analysis in its series Working Paper Series with number 46_13.

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Date of creation: Aug 2013
Handle: RePEc:rim:rimwps:46_13
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  1. Olivier Scaillet, 2005. "A Kolmogorov-Smirnov Type Test for Positive Quadrant Dependence," FAME Research Paper Series rp128, International Center for Financial Asset Management and Engineering.
  2. Chen, Xiaohong & Fan, Yanqin & Tsyrennikov, Viktor, 2006. "Efficient Estimation of Semiparametric Multivariate Copula Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1228-1240, September.
  3. Li, Qi & Racine, Jeffrey S, 2008. "Nonparametric Estimation of Conditional CDF and Quantile Functions With Mixed Categorical and Continuous Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 423-434.
  4. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.
  5. Trivedi, Pravin K. & Zimmer, David M., 2007. "Copula Modeling: An Introduction for Practitioners," Foundations and Trends(R) in Econometrics, now publishers, vol. 1(1), pages 1-111, April.
  6. Xiaohong Chen & Wei Biao Wu Wu & Yanping Yi, 2009. "Efficient estimation of copula-based semiparametric Markov models," CeMMAP working papers CWP06/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  7. Jean-David FERMANIAN & Olivier SCAILLET, 2003. "Nonparametric Estimation of Copulas for Time Series," FAME Research Paper Series rp57, International Center for Financial Asset Management and Engineering.
  8. H. G. Müller & U. Stadtmüller, 1999. "Multivariate boundary kernels and a continuous least squares principle," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 439-458.
  9. Nikolay Nenovsky & S. Statev, 2006. "Introduction," Post-Print halshs-00260898, HAL.
  10. Li, Qi & Racine, Jeff, 2003. "Nonparametric estimation of distributions with categorical and continuous data," Journal of Multivariate Analysis, Elsevier, vol. 86(2), pages 266-292, August.
  11. 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.
  12. Qi Li & Juan Lin & Jeffrey S. Racine, 2013. "Optimal Bandwidth Selection for Nonparametric Conditional Distribution and Quantile Functions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(1), pages 57-65, January.
  13. Hayfield, Tristen & Racine, Jeffrey S., 2008. "Nonparametric Econometrics: The np Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i05).
  14. Xiaohong Chen & Wei Biao Wu & Yanping Yi, 2009. "Efficient Estimation of Copula-based Semiparametric Markov Models," Cowles Foundation Discussion Papers 1691, Cowles Foundation for Research in Economics, Yale University, revised Mar 2009.
  15. Michel Denuit, 2004. "Nonparametric Tests for Positive Quadrant Dependence," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(3), pages 422-450.
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