On Some Mixing Properties of Copula-Based Markov Chains

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. We 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 generates psi-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-mixing.