On some mixing properties of copula-based Markov chains

11/29/2021

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by   Martial Longla, et al.

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This paper brings some insights of ψ'-mixing, ψ^*-mixing and ψ-mixing for copula-based Markov chains and the perturbations of their copulas. We provide new tools to check Markov chains for ψ-mixing or ψ'-mixing, and also show that perturbations of ψ'-mixing copula-based Markov chains are ψ'-mixing while perturbations of ψ-mixing Markov chains are not necessarily ψ-mixing Markov chains, even when the perturbed copula is ψ-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 ψ-mixing.