On Dependence Structure of Copula-based Markov chains

TL;DR

This paper investigates the dependence structures of copula-based Markov chains, providing new theoretical insights, conditions for exponential mixing, and analysis of specific copula families.

Contribution

It offers improved results on dependence coefficients, a necessary condition for exponential $ ho$-mixing in Archimedean copula-based chains, and analyzes specific copula examples.

Findings

Reversible Markov chains have certain equivalencies in dependence coefficients.

A necessary condition for exponential $ ho$-mixing in Archimedean copula chains is established.

Analysis of Mardia and Frechet copula families using small sets.

Abstract

We consider dependence coefficients for stationary Markov chains. We emphasize on some equivalencies for reversible Markov chains. We improve some known results and provide a necessary condition for Markov chains based on Archimedean copulas to be exponential $\rho$-mixing. We analyze the example of the Mardia and Frechet copula families using small sets.