Copulas and Temporal Dependence


  • Brendan K. Beare

    1. Dept. of Economics, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0508, U.S.A.;
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    • Parts of this paper derive from my doctoral research at Yale University. I thank my advisor Peter Phillips and committee members Donald Andrews and Yuichi Kitamura for their support and advice. I also thank Xiaohong Chen, Rustam Ibragimov, Bent Nielsen, Andres Santos, and three anonymous referees for helpful comments. Financial support from the Cowles Foundation under a Carl Arvid Anderson Prize Fellowship is gratefully acknowledged.


An emerging literature in time series econometrics concerns the modeling of potentially nonlinear temporal dependence in stationary Markov chains using copula functions. We obtain sufficient conditions for a geometric rate of mixing in models of this kind. Geometric β-mixing is established under a rather strong sufficient condition that rules out asymmetry and tail dependence in the copula function. Geometric ρ-mixing is obtained under a weaker condition that permits both asymmetry and tail dependence. We verify one or both of these conditions for a range of parametric copula functions that are popular in applied work.