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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.

Please cite this article as: M. Longla, On mixtures of copulas and mixing coefficients, Journal of Multivariate Analysis (2015), http://dx. AbstractWe show that if the density of the absolutely continuous part of a copula is bounded away from zero on a set of Lebesgue measure 1, then that copula generates "lower ψ-mixing" stationary Markov chains. This conclusion implies φ-mixing, ρ-mixing, β-mixing and "interlaced ρ-mixing". We also provide some new results on the mixing structure of Markov chains generated by mixtures of copulas.

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In this paper, we study dependence coefficients for copula-based Markov chains. We provide new tools to check the convergence rates of mixing coefficients of copula-based Markov chains. We study Markov chains generated by the Metropolis-hastings algorithm and give conditions on the proposal that ensure exponential ρ-mixing, β-mixing and φ-mixing. A general necessary condition on symmetric copulas to generate exponential ρ-mixing or φ-mixing is given. At the end of the paper, we comment and improve some of our previous results on mixtures of copulas.