Estimation and Forecasting of Dynamic Conditional Covariance: A Semiparametric Multivariate Model Variables with Econometric Applications

We propose a semiparametric conditional covariance (SCC) estimator that combines the ï¬rst-stage parametric conditional covariance (PCC) estimator with the second-stage nonparametric correction estimator in a multiplicative way. We prove the asymptotic normality of our SCC estimator, propose a nonparametric test for the correct speciï¬cation of PCC models, and study its asymptotic properties. We evaluate the ï¬nite sample performance of our test and SCC estimator and compare the latter with that of PCC estimator, purely nonparametric estimator, and Hafner, Dijk, and Franses’s (2006) estimator in terms of mean squared error and Value-at-Risk losses via simulations and real data analyses.