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On mixtures of copulas and mixing coefficients

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  • Longla, Martial

Abstract

We show that if the density of the absolutely continuous part of a copula is bounded away from zero on a set of Lebesgue measure 1, then that copula generates “lower ψ-mixing” stationary Markov chains. This conclusion implies ϕ-mixing, ρ-mixing, β-mixing and “interlaced ρ-mixing”. We also provide some new results on the mixing structure of Markov chains generated by mixtures of copulas.

Suggested Citation

  • Longla, Martial, 2015. "On mixtures of copulas and mixing coefficients," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 259-265.
    • Handle: RePEc:eee:jmvana:v:139:y:2015:i:c:p:259-265
    DOI: 10.1016/j.jmva.2015.03.009
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    References listed on IDEAS

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    1. Beare, Brendan K., 2012. "Archimedean Copulas And Temporal Dependence," Econometric Theory, Cambridge University Press, vol. 28(6), pages 1165-1185, December.
    2. Brendan K. Beare, 2010. "Copulas and Temporal Dependence," Econometrica, Econometric Society, vol. 78(1), pages 395-410, January.
    3. Bradley, Richard C., 1997. "Every "lower psi-mixing" Markov chain is "interlaced rho-mixing"," Stochastic Processes and their Applications, Elsevier, vol. 72(2), pages 221-239, December.
    4. Longla, Martial & Peligrad, Magda, 2012. "Some aspects of modeling dependence in copula-based Markov chains," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 234-240.
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    Cited by:

    1. Shulin Zhang & Qian M. Zhou & Huazhen Lin, 2021. "Goodness-of-fit test of copula functions for semi-parametric univariate time series models," Statistical Papers, Springer, vol. 62(4), pages 1697-1721, August.
    2. Longla, Martial & Muia Nthiani, Mathias & Djongreba Ndikwa, Fidel, 2022. "Dependence and mixing for perturbations of copula-based Markov chains," Statistics & Probability Letters, Elsevier, vol. 180(C).

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