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On non-central squared copulas

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  • Nasri, Bouchra R.

Abstract

The goal of this paper is to introduce new families of multivariate copulas, extending the chi-square copulas, the Fisher copula, and squared copulas. The new families are constructed from existing copulas by first transforming their margins to standard Gaussian distributions, then transforming these variables into non-central chi-square variables with one degree of freedom, and finally by considering the copula associated with these new variables. It is shown that by varying the non-centrality parameters, one can model non-monotonic dependence, and when one or many non-centrality parameters are outside a given hyper-rectangle, then the copula is almost the same as the one when these parameters are infinite. For these new families, the tail behavior, the monotonicity of dependence measures such as Kendall’s tau and Spearman’s rho are investigated, and estimation is discussed. The R package NCSCopula (Nasri, 2019) can be used to estimate the parameters for several copula families.

Suggested Citation

  • Nasri, Bouchra R., 2020. "On non-central squared copulas," Statistics & Probability Letters, Elsevier, vol. 161(C).
    • Handle: RePEc:eee:stapro:v:161:y:2020:i:c:s0167715220300079
    DOI: 10.1016/j.spl.2020.108704
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    References listed on IDEAS

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    1. Nasri, Bouchra R. & Rémillard, Bruno N. & Bouezmarni, Taoufik, 2019. "Semi-parametric copula-based models under non-stationarity," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 347-365.
    2. Quessy, Jean-François & Rivest, Louis-Paul & Toupin, Marie-Hélène, 2016. "On the family of multivariate chi-square copulas," Journal of Multivariate Analysis, Elsevier, vol. 152(C), pages 40-60.
    3. Anne‐Catherine Favre & Jean‐François Quessy & Marie‐Hélène Toupin, 2018. "The new family of Fisher copulas to model upper tail dependence and radial asymmetry: Properties and application to high‐dimensional rainfall data," Environmetrics, John Wiley & Sons, Ltd., vol. 29(3), May.
    4. Brechmann, Eike Christian & Schepsmeier, Ulf, 2013. "Modeling Dependence with C- and D-Vine Copulas: The R Package CDVine," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 52(i03).
    5. Oh, Dong Hwan & Patton, Andrew J., 2016. "High-dimensional copula-based distributions with mixed frequency data," Journal of Econometrics, Elsevier, vol. 193(2), pages 349-366.
    6. Quessy, Jean-François & Durocher, Martin, 2019. "The class of copulas arising from squared distributions: Properties and inference," Econometrics and Statistics, Elsevier, vol. 12(C), pages 148-166.
    7. Holger Dette & Ria Van Hecke & Stanislav Volgushev, 2014. "Some Comments on Copula-Based Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1319-1324, September.
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    Cited by:

    1. Nasri, Bouchra R., 2022. "Tests of serial dependence for multivariate time series with arbitrary distributions," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    2. Bücher Axel & Jaser Miriam & Min Aleksey, 2021. "Detecting departures from meta-ellipticity for multivariate stationary time series," Dependence Modeling, De Gruyter, vol. 9(1), pages 121-140, January.

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