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Continuous Exchangeable Markov Chains, Idempotent and 1-Dependent Copulas

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  • Martial Longla

    (Department of mathematics, College of Liberal Arts, University of Mississippi, University, MS 38677, USA)

Abstract

New copula families are constructed based on orthogonality in L 2 ( 0 , 1 ) . Subclasses of idempotent copulas with square integrable densities are derived. It is shown that these copulas generate exchangeable Markov chains that behave as independent and identically distributed random variables conditionally on the initial variable. We prove that the extracted family of copulas is the only set of symmetric idempotent copulas with square integrable densities. We extend these copula families to asymmetric copulas with square integrable densities having special dependence properties. One of our extensions includes the Farlie–Gumbel–Morgenstern (FGM) copula family. The mixing properties of Markov chains generated by these copulas are established. The Spearman’s correlation coefficient ρ S is provided for each of these copula families. Some graphs are also provided to illustrate the properties of the copula densities.

Suggested Citation

  • Martial Longla, 2025. "Continuous Exchangeable Markov Chains, Idempotent and 1-Dependent Copulas," Mathematics, MDPI, vol. 13(12), pages 1-22, June.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:12:p:2034-:d:1683080
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    References listed on IDEAS

    as
    1. Magda Peligrad, 2024. "On the Quenched CLT for Stationary Markov Chains," Journal of Theoretical Probability, Springer, vol. 37(1), pages 603-622, March.
    2. Longla, Martial, 2015. "On mixtures of copulas and mixing coefficients," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 259-265.
    3. Martial Longla, 2024. "New copula families and mixing properties," Statistical Papers, Springer, vol. 65(7), pages 4331-4363, September.
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