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Dependence and mixing for perturbations of copula-based Markov chains

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  • Longla, Martial
  • Muia Nthiani, Mathias
  • Djongreba Ndikwa, Fidel

Abstract

This paper explores the impact of perturbations of copulas on dependence properties of the Markov chains they generate. We use an observation that is valid for convex combinations of copulas to establish sufficient conditions for the mixing coefficients ρn, αn and some other measures of association. New copula families are derived based on perturbations of copulas and their multivariate analogs for n-copulas are provided in general. Several families of copulas can be constructed from the provided framework.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:stapro:v:180:y:2022:i:c:s0167715221002017
    DOI: 10.1016/j.spl.2021.109239
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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. Ibragimov, Rustam, 2009. "Copula-Based Characterizations For Higher Order Markov Processes," Econometric Theory, Cambridge University Press, vol. 25(3), pages 819-846, June.
    3. Brendan K. Beare, 2010. "Copulas and Temporal Dependence," Econometrica, Econometric Society, vol. 78(1), pages 395-410, January.
    4. Merlevède, Florence & Peligrad, Magda, 2020. "Functional CLT for nonstationary strongly mixing processes," Statistics & Probability Letters, Elsevier, vol. 156(C).
    5. Longla, Martial, 2015. "On mixtures of copulas and mixing coefficients," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 259-265.
    6. 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. Zachariah, Swaroop Georgy & Arshad, Mohd. & Pathak, Ashok Kumar, 2024. "A new class of copulas having dependence range larger than FGM-type copulas," Statistics & Probability Letters, Elsevier, vol. 206(C).

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