Efficient estimation of copula-based semiparametric Markov models

Xiaohong Chen (), Wei Biao Wu Wu and Yanping Yi
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Wei Biao Wu Wu: Institute for Fiscal Studies
Yanping Yi: Institute for Fiscal Studies

No CWP06/09, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

Abstract: This paper considers efficient estimation of copula-based semiparametric strictly stationary Markov models. These models are characterized by nonparametric invariant distributions and parametric copula functions; where the copulas capture all scale-free temporal dependence and tail dependence of the processes. The Markov models 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 (with tail dependence) are all geometric 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 the sieve likelihood ratio statistics is 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 by Clayton, Gumbel and other copulas having strong tail dependence.

JEL-codes: C14 C22 (search for similar items in EconPapers)
Date: 2009-03-03
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (39)

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Working Paper: Efficient Estimation of Copula-based Semiparametric Markov Models (2009)
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