Efficient Estimation of Copula-based Semiparametric Markov Models

Xiaohong Chen (), Wei Biao Wu and Yanping Yi
Additional contact information
Wei Biao Wu: Dept. of Statistics, University of Chicago
Yanping Yi: Dept of Economics, New York University

No 1691, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: This paper considers 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 functionals are root-$n$ consistent, asymptotically normal and efficient; and that their sieve likelihood ratio statistics are asymptotically chi-square distributed. We present Monte Carlo studies to compare the finite sample performance of the sieve MLE, the two-step estimator of Chen and Fan (2006), the correctly specified parametric MLE and the incorrectly specified parametric MLE. The simulation results indicate that our sieve MLEs perform very well; having much smaller biases and smaller variances than the two-step estimator for Markov models generated via Clayton, Gumbel and other tail dependent copulas.

Keywords: Copula; Tail dependence; Nonlinear Markov models; Geometric ergodicity; Sieve MLE; Semiparametric efficiency; Sieve likelihood ratio statistics; Value-at-Risk (search for similar items in EconPapers)
JEL-codes: C14 C22 (search for similar items in EconPapers)
Pages: 55 pages
Date: 2009-02, Revised 2009-03
New Economics Papers: this item is included in nep-ecm, nep-ore and nep-rmg
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (44)

Published in Annals of Statistics (2009), 37(6B): 4214-4253

Downloads: (external link)
https://cowles.yale.edu/sites/default/files/files/pub/d16/d1691.pdf (application/pdf)
Our link check indicates that this URL is bad, the error code is: 404 Not Found

Related works:
Working Paper: Efficient estimation of copula-based semiparametric Markov models (2009)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:cwl:cwldpp:1691

Ordering information: This working paper can be ordered from
Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA
The price is None.

Access Statistics for this paper

More papers in Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University Yale University, Box 208281, New Haven, CT 06520-8281 USA. Contact information at EDIRC.
Bibliographic data for series maintained by Brittany Ladd ().