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Tail-weighted measures of dependence

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  • Pavel Krupskii
  • Harry Joe

Abstract

Multivariate copula models are commonly used in place of Gaussian dependence models when plots of the data suggest tail dependence and tail asymmetry. In these cases, it is useful to have simple statistics to summarize the strength of dependence in different joint tails. Measures of monotone association such as Kendall's tau and Spearman's rho are insufficient to distinguish commonly used parametric bivariate families with different tail properties. We propose lower and upper tail-weighted bivariate measures of dependence as additional scalar measures to distinguish bivariate copulas with roughly the same overall monotone dependence. These measures allow the efficient estimation of strength of dependence in the joint tails and can be used as a guide for selection of bivariate linking copulas in vine and factor models as well as for assessing the adequacy of fit of multivariate copula models. We apply the tail-weighted measures of dependence to a financial data set and show that the measures better discriminate models with different tail properties compared to commonly used risk measures - the portfolio value-at-risk and conditional tail expectation.

Suggested Citation

  • Pavel Krupskii & Harry Joe, 2015. "Tail-weighted measures of dependence," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(3), pages 614-629, March.
    • Handle: RePEc:taf:japsta:v:42:y:2015:i:3:p:614-629
    DOI: 10.1080/02664763.2014.980787
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    References listed on IDEAS

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    Cited by:

    1. Nguyen, Hoang & Ausín, M. Concepción & Galeano, Pedro, 2020. "Variational inference for high dimensional structured factor copulas," Computational Statistics & Data Analysis, Elsevier, vol. 151(C).
    2. Kreuzer, Alexander & Dalla Valle, Luciana & Czado, Claudia, 2023. "Bayesian multivariate nonlinear state space copula models," Computational Statistics & Data Analysis, Elsevier, vol. 188(C).
    3. Krupskii, Pavel & Genton, Marc G., 2019. "A copula model for non-Gaussian multivariate spatial data," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 264-277.
    4. Shogo Kato & Toshinao Yoshiba & Shinto Eguchi, 2022. "Copula-based measures of asymmetry between the lower and upper tail probabilities," Statistical Papers, Springer, vol. 63(6), pages 1907-1929, December.
    5. Krupskii, Pavel & Joe, Harry & Lee, David & Genton, Marc G., 2018. "Extreme-value limit of the convolution of exponential and multivariate normal distributions: Link to the Hüsler–Reiß distribution," Journal of Multivariate Analysis, Elsevier, vol. 163(C), pages 80-95.
    6. Pavel Krupskii, 2017. "Copula-based measures of reflection and permutation asymmetry and statistical tests," Statistical Papers, Springer, vol. 58(4), pages 1165-1187, December.
    7. Tarik Bahraoui & Nikolai Kolev, 2021. "New Measure of the Bivariate Asymmetry," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 421-448, February.
    8. Krupskii, Pavel & Joe, Harry, 2020. "Flexible copula models with dynamic dependence and application to financial data," Econometrics and Statistics, Elsevier, vol. 16(C), pages 148-167.

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