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Mixed Data Kernel Copulas

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  • Jeffrey S. Racine

    (McMaster University, Canada)

Abstract

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).

Suggested Citation

  • Jeffrey S. Racine, 2013. "Mixed Data Kernel Copulas," Working Paper series 46_13, Rimini Centre for Economic Analysis.
  • Handle: RePEc:rim:rimwps:46_13
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    References listed on IDEAS

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    1. Rong Liu & Lijian Yang, 2008. "Kernel estimation of multivariate cumulative distribution function," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(8), pages 661-677.
    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.
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    4. 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.
    5. 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.
    6. 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.
    7. Cong Li & Hongjun Li & Jeffrey S. Racine, 2017. "Cross-validated mixed-datatype bandwidth selection for nonparametric cumulative distribution/survivor functions," Econometric Reviews, Taylor & Francis Journals, vol. 36(6-9), pages 970-987, October.
    8. Luc Bauwens & Sébastien Laurent & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109, January.
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    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. Hayfield, Tristen & Racine, Jeffrey S., 2008. "Nonparametric Econometrics: The np Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i05).
    13. 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.
    14. 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.
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    Cited by:

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    3. Fousekis, Panos & Grigoriadis, Vasilis, 2017. "Price co-movement and the crack spread in the US futures markets," Journal of Commodity Markets, Elsevier, vol. 7(C), pages 57-71.
    4. Wadud, Sania & Gronwald, Marc & Durand, Robert B. & Lee, Seungho, 2023. "Co-movement between commodity and equity markets revisited—An application of the Thick Pen method," International Review of Financial Analysis, Elsevier, vol. 87(C).
    5. Stelios Bekiros & Gazi Salah Uddin, 2017. "Extreme Dependence under Uncertainty: an application to Stock, Currency and Oil Markets," International Review of Finance, International Review of Finance Ltd., vol. 17(1), pages 155-162, March.
    6. Fousekis, Panos, 2017. "Price co-movement and the hedger's value-at-risk in the futures markets for coffee," Agricultural Economics Review, Greek Association of Agricultural Economists, vol. 0(Issue 1), January.
    7. Kang, Sang Hoon & Uddin, Gazi Salah & Ahmed, Ali & Yoon, Seong-Min, 2018. "Multi-scale causality and extreme tail inter-dependence among housing prices," Economic Modelling, Elsevier, vol. 70(C), pages 301-309.
    8. Ho, Anson T.Y. & Huynh, Kim P. & Jacho-Chávez, David T., 2019. "Using nonparametric copulas to measure crude oil price co-movements," Energy Economics, Elsevier, vol. 82(C), pages 211-223.
    9. Fousekis, Panos & Grigoriadis, Vasilis, 2016. "Spatial price dependence by time scale: Empirical evidence from the international butter markets," Economic Modelling, Elsevier, vol. 54(C), pages 195-204.

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