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Asymptotic properties of the Bernstein density copula estimator for [alpha]-mixing data

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  • Bouezmarni, Taoufik
  • Rombouts, Jeroen V.K.
  • Taamouti, Abderrahim

Abstract

Copulas are extensively used for dependence modeling. In many cases the data does not reveal how the dependence can be modeled using a particular parametric copula. Nonparametric copulas do not share this problem since they are entirely data based. This paper proposes nonparametric estimation of the density copula for [alpha]-mixing data using Bernstein polynomials. We focus only on the dependence structure between stochastic processes, captured by the copula density defined on the unit cube, and not the complete distribution. We study the asymptotic properties of the Bernstein density copula, i.e., we provide the exact asymptotic bias and variance, we establish the uniform strong consistency and the asymptotic normality. An empirical application is considered to illustrate the dependence structure among international stock markets (US and Canada) using the Bernstein density copula estimator.

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  • Bouezmarni, Taoufik & Rombouts, Jeroen V.K. & Taamouti, Abderrahim, 2010. "Asymptotic properties of the Bernstein density copula estimator for [alpha]-mixing data," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 1-10, January.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:1:p:1-10
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    Cited by:

    1. Ouimet, Frédéric, 2021. "Asymptotic properties of Bernstein estimators on the simplex," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    2. Taamouti, Abderrahim & Bouezmarni, Taoufik & El Ghouch, Anouar, 2014. "Nonparametric estimation and inference for conditional density based Granger causality measures," Journal of Econometrics, Elsevier, vol. 180(2), pages 251-264.
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    4. Taoufik Bouezmarni & Jeroen V.K. Rombouts & Abderrahim Taamouti, 2011. "Nonparametric Copula-Based Test for Conditional Independence with Applications to Granger Causality," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(2), pages 275-287, October.
    5. Taoufik Bouezmarni & Mohamed Doukali & Abderrahim Taamouti, 2023. "Copula-based estimation of health inequality measures with an application to COVID-19," University of East Anglia School of Economics Working Paper Series 2023-01, School of Economics, University of East Anglia, Norwich, UK..
    6. Bouezmarni Taoufik & Ghouch El & Taamouti Abderrahim, 2013. "Bernstein estimator for unbounded copula densities," Statistics & Risk Modeling, De Gruyter, vol. 30(4), pages 343-360, December.
    7. Janssen, Paul & Swanepoel, Jan & Veraverbeke, Noël, 2014. "A note on the asymptotic behavior of the Bernstein estimator of the copula density," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 480-487.
    8. Taamouti, Abderrahim & Bouezmarni, Taoufik & El Ghouch, Anouar, 2012. "Nonparametric Estimation and Inference for Granger Causality Measures," LIDAM Discussion Papers ISBA 2012009, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    9. Noh, Hohsuk & El Ghouch, Anouar & Bouezmarni, Taoufik, 2012. "Copula-Based Regression Estimation and Inference," LIDAM Discussion Papers ISBA 2012010, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    10. Bouezmarni, Taoufik & El Ghouch, Anouar, 2011. "Bernstein estimator for unbounded density copula," UC3M Working papers. Economics we1143, Universidad Carlos III de Madrid. Departamento de Economía.
    11. Berghaus, Betina & Segers, Johan, 2018. "Weak convergence of the weighted empirical beta copula process," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 266-281.
    12. Mirza Nazmul Hasan & Roel Braekers, 2022. "Modelling the association in bivariate survival data by using a Bernstein copula," Computational Statistics, Springer, vol. 37(2), pages 781-815, April.
    13. Eddie Anderson & Artem Prokhorov & Yajing Zhu, 2020. "A Simple Estimator of Two‐Dimensional Copulas, with Applications," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 82(6), pages 1375-1412, December.
    14. Gery Geenens & Arthur Charpentier & Davy Paindaveine, 2014. "Probit Transformation for Nonparametric Kernel Estimation of the Copula Density," Working Papers ECARES ECARES 2014-23, ULB -- Universite Libre de Bruxelles.
    15. Taoufik Bouezmarni & Mohamed Doukali & Abderrahim Taamouti, 2022. "Copula-based estimation of health concentration curves with an application to COVID-19," CIRANO Working Papers 2022s-07, CIRANO.
    16. Okhrin Ostap, 2013. "Editorial to the special issue on Copulae of Statistics & Risk Modeling," Statistics & Risk Modeling, De Gruyter, vol. 30(4), pages 281-286, December.

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