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Copula-based measures of asymmetry between the lower and upper tail probabilities

Author

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  • Shogo Kato

    (Institute of Statistical Mathematics)

  • Toshinao Yoshiba

    (Tokyo Metropolitan University)

  • Shinto Eguchi

    (Institute of Statistical Mathematics)

Abstract

We propose a copula-based measure of asymmetry between the lower and upper tail probabilities of bivariate distributions. The proposed measure has a simple form and possesses some desirable properties as a measure of asymmetry. The limit of the proposed measure as the index goes to the boundary of its domain can be expressed in a simple form under certain conditions on copulas. A sample analogue of the proposed measure for a sample from a copula is presented and its weak convergence to a Gaussian process is shown. Another sample analogue of the presented measure, which is based on a sample from a distribution on $$\mathbb {R}^2$$ R 2 , is given. Simple methods for interval and region estimation are presented. A simulation study is carried out to investigate the performance of the proposed sample analogues and methods for interval estimation. As an example, the presented measure is applied to daily returns of S&P500 and Nikkei225. A trivariate extension of the proposed measure and its sample analogue are briefly discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:63:y:2022:i:6:d:10.1007_s00362-022-01297-w
    DOI: 10.1007/s00362-022-01297-w
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    References listed on IDEAS

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