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Estimating copula densities through wavelets

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  • Genest, Christian
  • Masiello, Esterina
  • Tribouley, Karine

Abstract

Wavelet analysis is used to construct a rank-based estimator of a copula density. The procedure, which can be easily implemented with ready-to-use wavelet packages, is based on an algorithm that handles boundary effects automatically. The resulting estimator provides a non-parametric benchmark for the selection of a parametric copula family. From a theoretical point of view, the estimation procedure is shown to be optimal in the minimax sense on a large functional class of regular copula densities. The approach is illustrated with actuarial and financial data.

Suggested Citation

  • Genest, Christian & Masiello, Esterina & Tribouley, Karine, 2009. "Estimating copula densities through wavelets," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 170-181, April.
    • Handle: RePEc:eee:insuma:v:44:y:2009:i:2:p:170-181
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    Cited by:

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    2. Morettin Pedro A. & Toloi Clelia M.C. & Chiann Chang & de Miranda José C.S., 2011. "Wavelet Estimation of Copulas for Time Series," Journal of Time Series Econometrics, De Gruyter, vol. 3(3), pages 1-31, October.
    3. Jean-David Fermanian, 2012. "An overview of the goodness-of-fit test problem for copulas," Papers 1211.4416, arXiv.org.
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    5. Pedro Alberto Morettin & Clélia Maria de Castro Toloi & Chang Chiann & José Carlos Simon de Miranda, 2010. "Wavelet Smoothed Empirical Copula Estimators," Brazilian Review of Finance, Brazilian Society of Finance, vol. 8(3), pages 263-281.
    6. Di Bernardino Elena & Rullière Didier, 2013. "On certain transformations of Archimedean copulas: Application to the non-parametric estimation of their generators," Dependence Modeling, De Gruyter, vol. 1, pages 1-36, October.
    7. Boubaker, Heni & Sghaier, Nadia, 2013. "Portfolio optimization in the presence of dependent financial returns with long memory: A copula based approach," Journal of Banking & Finance, Elsevier, vol. 37(2), pages 361-377.
    8. Khalfaoui, R. & Boutahar, M. & Boubaker, H., 2015. "Analyzing volatility spillovers and hedging between oil and stock markets: Evidence from wavelet analysis," Energy Economics, Elsevier, vol. 49(C), pages 540-549.
    9. O. Chatrabgoun & G. Parham & R. Chinipardaz, 2017. "A Legendre multiwavelets approach to copula density estimation," Statistical Papers, Springer, vol. 58(3), pages 673-690, September.
    10. Autin, F. & Le Pennec, E. & Tribouley, K., 2010. "Thresholding methods to estimate copula density," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 200-222, January.
    11. Nagler, Thomas & Czado, Claudia, 2016. "Evading the curse of dimensionality in nonparametric density estimation with simplified vine copulas," Journal of Multivariate Analysis, Elsevier, vol. 151(C), pages 69-89.
    12. Qureshi, Saba & Rehman, Ijaz Ur & Qureshi, Fiza, 2018. "Does gold act as a safe haven against exchange rate fluctuations? The case of Pakistan rupee," Journal of Policy Modeling, Elsevier, vol. 40(4), pages 685-708.
    13. Faugeras, Olivier P., 2009. "A quantile-copula approach to conditional density estimation," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2083-2099, October.
    14. Derrode, Stéphane & Pieczynski, Wojciech, 2013. "Unsupervised data classification using pairwise Markov chains with automatic copulas selection," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 81-98.
    15. 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.
    16. Akakpo, Nathalie, 2017. "Multivariate intensity estimation via hyperbolic wavelet selection," Journal of Multivariate Analysis, Elsevier, vol. 161(C), pages 32-57.

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