Estimation and Forecasting of Dynamic Conditional Covariance: A Semiparametric Multivariate Model

The existing parametric multivariate generalized autoregressive conditional heteroskedasticity (MGARCH) model could hardly capture the nonlinearity and the non-normality, which are widely observed in …nancial data. We propose semiparametric conditional covariance (SCC) model to capture the information hidden in the standardized residuals and missed by the parametric MGARCH models. Our two-stage SCC estimator incorporates the parametric and nonparametric estimators of the conditional covariance in a multiplicative way. We prove the consistency and asymptotic normality of our semiparametric estimator. We conduct a small set of Monte Carlo experiments to demonstrate the advantage of our SCC estimators over their parametric counterparts in terms of mean squared error. For both in-sample …tting and out-of-sample forecasting conditional covariance matrix, our SCC models also outperform the parametric ones in empirical applications on bivariate stock indices and two stock portfolios with thirty underlying stocks. JEL Classi…cations: C3; C5; G0