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New copula families and mixing properties

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  • Martial Longla

    (University of Mississippi)

Abstract

We characterize absolutely continuous symmetric copulas with square integrable densities in this paper. This characterization is used to create new copula families, that are perturbations of the independence copula. The full study of mixing properties of Markov chains generated by these copula families is conducted. An extension that includes the Farlie–Gumbel–Morgenstern family of copulas is proposed. We propose some examples of copulas that generate non-mixing Markov chains, but whose convex combinations generate $$\psi $$ ψ -mixing Markov chains. Some general results on $$\psi $$ ψ -mixing are given. The Spearman’s correlation $$\rho _S$$ ρ S and Kendall’s $$\tau $$ τ are provided for the created copula families. Some general remarks are provided for $$\rho _S$$ ρ S and $$\tau $$ τ . A central limit theorem is provided for parameter estimators in one example. A simulation study is conducted to support derived asymptotic distributions for some examples.

Suggested Citation

  • Martial Longla, 2024. "New copula families and mixing properties," Statistical Papers, Springer, vol. 65(7), pages 4331-4363, September.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:7:d:10.1007_s00362-024-01559-9
    DOI: 10.1007/s00362-024-01559-9
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    References listed on IDEAS

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    6. Longla, Martial, 2015. "On mixtures of copulas and mixing coefficients," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 259-265.
    7. 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.
    8. Paul Doukhan & Jean-David Fermanian & Gabriel Lang, 2009. "An empirical central limit theorem with applications to copulas under weak dependence," Statistical Inference for Stochastic Processes, Springer, vol. 12(1), pages 65-87, February.
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