Open Access
December 2009 Efficient estimation of copula-based semiparametric Markov models
Xiaohong Chen, Wei Biao Wu, Yanping Yi
Ann. Statist. 37(6B): 4214-4253 (December 2009). DOI: 10.1214/09-AOS719


This paper considers the efficient estimation of copula-based semiparametric strictly stationary Markov models. These models are characterized by nonparametric invariant (one-dimensional marginal) distributions and parametric bivariate copula functions where the copulas capture temporal dependence and tail dependence of the processes. The Markov processes generated via tail dependent copulas may look highly persistent and are useful for financial and economic applications. We first show that Markov processes generated via Clayton, Gumbel and Student’s t copulas and their survival copulas are all geometrically ergodic. We then propose a sieve maximum likelihood estimation (MLE) for the copula parameter, the invariant distribution and the conditional quantiles. We show that the sieve MLEs of any smooth functional is root-n consistent, asymptotically normal and efficient and that their sieve likelihood ratio statistics are asymptotically chi-square distributed. Monte Carlo studies indicate that, even for Markov models generated via tail dependent copulas and fat-tailed marginals, our sieve MLEs perform very well.


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Xiaohong Chen. Wei Biao Wu. Yanping Yi. "Efficient estimation of copula-based semiparametric Markov models." Ann. Statist. 37 (6B) 4214 - 4253, December 2009.


Published: December 2009
First available in Project Euclid: 23 October 2009

zbMATH: 1191.62140
MathSciNet: MR2572458
Digital Object Identifier: 10.1214/09-AOS719

Primary: 62M05
Secondary: 62F07

Keywords: copula , geometric ergodicity , nonlinear Markov models , Semiparametric efficiency , sieve likelihood ratio statistics , sieve MLE , tail dependence , value-at-risk

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 6B • December 2009
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