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arXiv · 2111.14682

On some mixing properties of copula-based Markov chains

Martial Longla·Mous-Abou Hamadou·Seraphin Isidore Ngongo
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Abstract

This paper brings some insights of $\psi'$-mixing, $\psi^*$-mixing and $\psi$-mixing for copula-based Markov chains and the perturbations of their copulas. We provide new tools to check Markov chains for $\psi$-mixing or $\psi'$-mixing, and also show that perturbations of $\psi'$-mixing copula-based Markov chains are $\psi'$-mixing while perturbations of $\psi$-mixing Markov chains are not necessarily $\psi$-mixing Markov chains, even when the perturbed copula is $\psi-mixing$. Some examples of copula families are considered. A statistical study is provided to emphasize the impact of perturbations on copula-based Markov chains. Moreover, we provide a correction to a statement made in Longla and al. (2021) on $\psi$-mixing.

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Martial Longla, Mous-Abou Hamadou, Seraphin Isidore Ngongo. 2021-11-29. On some mixing properties of copula-based Markov chains. https://arxiv.org/abs/2111.14682

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