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Efficient Estimation of Multivariate Semi-nonparametric GARCH Filtered Copula Models

Xiaohong Chen (), Zhuo Huang () and Yanping Yi ()
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Xiaohong Chen: Cowles Foundation, Yale University, https://sites.google.com/site/xiaohongchenyale/
Zhuo Huang: Peking University
Yanping Yi: School of Economics and Academy of Financial Research, Zhejiang University

No 2215, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: This paper considers estimation of semi-nonparametric GARCH ï¬ ltered copula models in which the individual time series are modelled by semi-nonparametric GARCH and the joint distributions of the multivariate standardized innovations are characterized by parametric copulas with nonparametric marginal distributions. The models extend those of Chen and Fan (2006) to allow for semi-nonparametric conditional means and volatilities, which are estimated via the method of sieves such as splines. The ï¬ tted residuals are then used to estimate the copula parameters and the marginal densities of the standardized innovations jointly via the sieve maximum likelihood (SML). We show that, even using nonparametrically ï¬ ltered data, both our SML and the two-step copula estimator of Chen and Fan (2006) are still root-n consistent and asymptotically normal, and the asymptotic variances of both estimators do not depend on the nonparametric ï¬ ltering errors. Even more surprisingly, our SML copula estimator using the ï¬ ltered data achieves the full semiparametric efficiency bound as if the standardized innovations were directly observed. These nice properties lead to simple and more accurate estimation of Value-at-Risk (VaR) for multivariate ï¬ nancial data with flexible dynamics, contemporaneous tail dependence and asymmetric distributions of innovations. Monte Carlo studies demonstrate that our SML estimators of the copula parameters and the marginal distributions of the standardized innovations have smaller variances and smaller mean squared errors compared to those of the two-step estimators in ï¬ nite samples. A real data application is presented.

Keywords: Semi-nonparametric dynamic models; Residual copulas; Semiparametric multistep; Residual sieve maximum likelihood; Semiparametric efficiency (search for similar items in EconPapers)
JEL-codes: C14 C22 G32 (search for similar items in EconPapers)
Pages: 78 pages
Date: 2019-10
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
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