On dependence structure of copula-based Markov chains

Department of Mathematics, University of Mississippi, University, MS 38677, USA
longla_m_martial@yahoo.com; mlongla@olemiss.edu

Received: 17 November 2012
Revised: 1 June 2013

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 ρ-mixing. We analyse the example of the Mardia and Frechet copula families using small sets.