Estimation of Multivariate Semiparametric GARCH Filtered Copula Models

Associate Professor, School of Economics, SUFE

Prof. Yanping Yi's CV

The semiparametric copula-based multivariate GARCH models of Chen and Fan (2006, Journal of Econometrics 135, 125-154) have been found very useful to quantify multivariate risks, in which univariate parametric or semiparametric GARCH models are used to model the temporal dependence of individual financial series, and parametric copulas are used to capture the contemporaneous dependence among semiparametric GARCH filtered residuals with nonparametric marginal distributions. In this paper, we analyze the effect of first stage estimation error on the estimation of copula parameters, which is important for statistical inference. In particular, for semiparametric / non-parametric GARCH filtered residuals, we address three questions (1)Will the asymptotic distribution of the two-step copula parameter estimator be affected by the first stage estimation error ? (2) How will the estimation of the dynamic GARCH parameters affect the sieve MLE of copula parameters? (3) Will the sieve MLE of copula parameters be more efficient than the two-step copula parameter estimator? Simulation studies are provided to examine the asymptotic properties and the finite sample performances of various estimators.