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.
Copulas and Temporal Dependence
Article first published online: 8 FEB 2010
© 2010 The Econometric Society
Volume 78, Issue 1, pages 395–410, January 2010
How to Cite
Beare, B. K. (2010), Copulas and Temporal Dependence. Econometrica, 78: 395–410. doi: 10.3982/ECTA8152
- Issue published online: 8 FEB 2010
- Article first published online: 8 FEB 2010
- Manuscript received September, 2008; final revision received June, 2009.
- Markov chain;
- maximal correlation;
- mean square contingency;
- canonical correlation;
- tail dependence
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.