Efficient Estimation of Copula-Based Semiparametric Markov Models

By Xiaohong Chen, Wei Biao Wu, Yanping Yi. 2009

102 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/2ec9e29f800d5e04685bc3274d343cc403efb933

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Finance

In Statistics and Probability

Citations in the corpus

COPULAS AND TEMPORAL DEPENDENCE (2008, background): “those of Chen et. al. (2009) , who establish a geometric rate of -mixing for Clayton, Gumbel and t-copulas.”
Sieve inference on possibly misspecified semi-nonparametric time series models (2014, background): “However, the sieve likelihood ratio inference given in Chen, Wu and Yi (2009) is no longer valid under misspecification.”
Copula Methods for Forecasting Multivariate Time Series (2013, unknown): “"itjFt 1 s Fi ( jZt 1; ) (30) or "itjFt 1 s iid Fi (31)”
Vine Copula Specifications for Stationary Multivariate Markov Chains (2015, background): “See, for instance, either of the textbooks by Cherubini et al. (2004, 2012), or any of the three review articles by Patton (2009, 2012, 2013). In a time series context, we may distinguish between the use of copulae to model contemporaneous relationships between multiple time series, and the use of c”
A review of copula models for economic time series (2012, background): “[29], Gagliardini and Gouriéroux [61], Ibragimov [95], and Ibragimov and Lentzas [96].”
Copulas in Econometrics (2014, background): “The majority of applications of copula-based multivariate models are in time series, so we make such models the focus of this section (for a discussion of copula-based univariate models, see, e.g., Darsow et al. 1992, Chen & Fan 2006b, Chen et al. 2009, Ibragimov 2009, Beare 2010).”