Perturbations of copulas and mixing properties

Longla, Martial; Ndikwa, Fidel Djongreba; Mathias, Muia,; Takam, Patrice Soh

doi:10.1007/s42952-021-00133-5

Cited by 4 publications

(10 citation statements)

References 16 publications

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“…References to this mixing can be found in Bradley [4]. A remark of Longla et al [15] states the following.…”

Section: Theorem 213 For Any Set Of Copulasmentioning

confidence: 88%

“…Komornik et al [13] have investigated some perturbations that were introduced by Mesiar et al [23]. These perturbations were also considered by Longla et al [15] and [16]. Perturbations that we consider in this work have been studied by many authors.…”

Section: About Perturbationsmentioning

confidence: 94%

“…It extends the result from -mixing to ′ -mixing. Longla et al [15] state that for a copula C perturbed by means of the independence copula Π , the following result holds for the perturbation copula C ,Π (u, v) with parameter .…”

Section: All About ã ′ -Mixingmentioning

confidence: 99%

“…In fact, they investigated the impact of perturbations of copulas on the mixing structure of the Markov chains that they generate. The case was presented for -mixing, -mixing, -mixing and -mixing in Longla et al [15] and [16]. Our work concerns the case of -mixing, ′ -mixing and * -mixing.…”

Section: Introductionmentioning

confidence: 97%

“…This justifies why dealing with the uniform distribution as stationary distribution of a Markov chain is same as studying a Markov chain with any absolutely continuous stationary distribution. Following the ideas of Durante et al [8], Longla et al [15] and Longla et al [16] have considered the perturbation method that adds to a copula an extra term called perturbation. They also considered other classes of modifications and their impact on the dependence structure as studied by Komornik et al [13].…”

Section: Introductionmentioning

confidence: 99%

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On Some Mixing Properties of Copula-Based Markov Chains

2022

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This paper brings some insights of $$\psi '$$ ψ ′ -mixing, $$\psi ^*$$ ψ ∗ -mixing and $$\psi$$ ψ -mixing for copula-based Markov chains and the perturbations of their copulas. We provide new tools to check Markov chains for $$\psi$$ ψ -mixing or $$\psi '$$ ψ ′ -mixing. We show that perturbations of $$\psi '$$ ψ ′ -mixing copula-based Markov chains are $$\psi '$$ ψ ′ -mixing while perturbations of $$\psi$$ ψ -mixing Markov chains are not necessarily $$\psi$$ ψ -mixing Markov chains, even when the perturbed copula generates $$\psi$$ ψ -mixing. The Farlie–Gumbel–Morgenstern, gaussian and Ali-Mikhail-Haq copula families are considered among other examples. A statistical study is provided to emphasize the impact of perturbations on copula-based Markov chains in a simulation study. Moreover, we provide a correction to a statement made in Longla et al. (J Korean Stat Soc, 1–23, 2021) on $$\psi$$ ψ -mixing.

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“…References to this mixing can be found in Bradley [4]. A remark of Longla et al [15] states the following.…”

Section: Theorem 213 For Any Set Of Copulasmentioning

confidence: 88%

Section: About Perturbationsmentioning

confidence: 94%

Section: All About ã ′ -Mixingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

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On Some Mixing Properties of Copula-Based Markov Chains

2022

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New copula families and mixing properties

Longla

2024

Stat Papers

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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.

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