Dependence and mixing for perturbations of copula-based Markov chains

TL;DR

This paper investigates how perturbations of copulas affect the dependence and mixing properties of the resulting Markov chains, introducing new copula families and conditions for mixing coefficients.

Contribution

It provides new theoretical conditions for dependence measures under copula perturbations and constructs novel copula families with multivariate extensions.

Findings

Established sufficient conditions for mixing coefficients under copula perturbations

Derived new copula families based on perturbations

Provided multivariate analogs for n-copulas

Abstract

This paper explores the impact of perturbations of copulas on dependence properties of the Markov chains they generate. We use an observation that is valid for convex combinations of copulas to establish sufficient conditions for the mixing coefficients $\rho_n$, $\alpha_n$ and some other measures of association. New copula families are derived based on perturbations of copulas and their multivariate analogs for $n$-copulas are provided in general. Several families of copulas can be constructed from the provided framework.