Efficient Estimation of Copula-based Semiparametric Markov Models

Xiaohong Chen (), Wei Biao Wu and Yanping Yi
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Xiaohong Chen: Cowles Foundation, Yale University, http://cowles.econ.yale.edu/faculty/chen.htm
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, 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)
New Economics Papers: this item is included in nep-ecm, nep-ore and nep-rmg
Date: 2009-02, Revised 2009-03
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Published in Annals of Statistics (2009), 37(6B): 4214-4253

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