Dependence and mixing for perturbations of copula-based Markov chains

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.