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Approximations of Copulas via Transformed Moments

Author

Listed:
  • Robert M. Mnatsakanov

    (West Virginia University)

  • Hansjoerg Albrecher

    (University of Lausanne
    Swiss Finance Institute)

  • Stephane Loisel

    (Laboratoire de Sciences Actuarielle et Financière, ISFA)

Abstract

We study the problem of approximating the copula and copula density function from a sequence of transformed moments. In particular, when frequency moments of an underlying bivariate distribution are available, the uniform convergence of the reconstructed copula and the rate of approximation of the copula density function are obtained. Finally, the accuracies of the approximation and estimation are illustrated in a simulation study.

Suggested Citation

  • Robert M. Mnatsakanov & Hansjoerg Albrecher & Stephane Loisel, 2022. "Approximations of Copulas via Transformed Moments," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 3175-3193, December.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:4:d:10.1007_s11009-022-09969-8
    DOI: 10.1007/s11009-022-09969-8
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    References listed on IDEAS

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    1. 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.
    2. Mnatsakanov, Robert M., 2008. "Hausdorff moment problem: Reconstruction of probability density functions," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1869-1877, September.
    3. 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.
    4. 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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