Efficient Estimation of Multivariate Semi-nonparametric GARCH Filtered Copula Models

78 Pages Posted: 26 Dec 2019

See all articles by Xiaohong Chen

Xiaohong Chen

Yale University - Cowles Foundation

Zhuo Huang

National School of Development, Peking University

Yanping Yi

Shanghai University of Finance and Economics - School of Economics

Date Written: October 6, 2019

Abstract

This paper considers estimation of semi-nonparametric GARCH filtered 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 fitted 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 filtered 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 filtering errors. Even more surprisingly, our SML copula estimator using the filtered 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 financial 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 finite samples. A real data application is presented.

Keywords: Semi-nonparametric dynamic models, Residual copulas, Semiparametric multistep, Residual sieve maximum likelihood, Semiparametric efficiency

JEL Classification: C14, C22, G32

Suggested Citation

Chen, Xiaohong and Huang, Zhuo and Yi, Yanping, Efficient Estimation of Multivariate Semi-nonparametric GARCH Filtered Copula Models (October 6, 2019). Cowles Foundation Discussion Paper No. 2215 (2019), Available at SSRN: https://ssrn.com/abstract=3509235 or http://dx.doi.org/10.2139/ssrn.3509235

Xiaohong Chen (Contact Author)

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States

Zhuo Huang

National School of Development, Peking University ( email )

No. 38 Xueyuan Road
Haidian District
Beijing, Beijing 100871
China

Yanping Yi

Shanghai University of Finance and Economics - School of Economics ( email )

777 Guoding Road
Shanghai, 200433
China

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