Efficient estimation of multivariate semi-nonparametric GARCH filtered copula models

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