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A Legendre multiwavelets approach to copula density estimation

Author

Listed:
  • O. Chatrabgoun

    (Malayer University)

  • G. Parham

    (Shahid Chamran University of Ahvaz)

  • R. Chinipardaz

    (Shahid Chamran University of Ahvaz)

Abstract

In this paper, a novel method for copula density estimation using Legendre multiwavelet is proposed. In general, copula density estimation methods based on the multiwavelet benefit from some useful properties, including they are symmetric, orthogonal and have compact support. In particular, the Legendre multiwavelet as a more general and vector-valued polynomial type of wavelets would results a more flexible and accurate approximation for the given copula density. In addition to high ability and nice properties of Legendre multiwavelet in approximation, its support is defined on unit interval, [0,1], as copulas that are normalized to have the support on the unit square and uniform marginal. We further make this approximation method more accurate by using multiresolution techniques. The comparative study reveals that the approximation proposed in this paper is more accurate than a scalar wavelet bases approximation. We eventually apply presented method to approximate multivariate distribution using pair-copula as a flexible multivariate copula to model a dataset of Norwegian financial data.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:58:y:2017:i:3:d:10.1007_s00362-015-0720-0
    DOI: 10.1007/s00362-015-0720-0
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    References listed on IDEAS

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    1. Genest, Christian & Masiello, Esterina & Tribouley, Karine, 2009. "Estimating copula densities through wavelets," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 170-181, April.
    2. Rada Dakovic & Claudia Czado, 2011. "Comparing point and interval estimates in the bivariate t-copula model with application to financial data," Statistical Papers, Springer, vol. 52(3), pages 709-731, August.
    3. 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.
    4. 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.
    5. Aas, Kjersti & Czado, Claudia & Frigessi, Arnoldo & Bakken, Henrik, 2009. "Pair-copula constructions of multiple dependence," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 182-198, April.
    6. Ulf Schepsmeier & Jakob Stöber, 2014. "Derivatives and Fisher information of bivariate copulas," Statistical Papers, Springer, vol. 55(2), pages 525-542, May.
    7. Biau, Gérard & Wegkamp, Marten, 2005. "A note on minimum distance estimation of copula densities," Statistics & Probability Letters, Elsevier, vol. 73(2), pages 105-114, June.
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    Cited by:

    1. Yu-Ye Zou & Han-Ying Liang, 2020. "CLT for integrated square error of density estimators with censoring indicators missing at random," Statistical Papers, Springer, vol. 61(6), pages 2685-2714, December.

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