Semiparametric Multivariate GARCH Model∗

To capture the missed information in the standardized errors by parametric multivariate generalized autoregressive conditional heteroskedasticity (MV-GARCH) model, we propose a new semiparametric MV-GARCH (SM-GARCH) model. This SM-GARCH model is a twostep model: firstly estimating parametric MV-GARCH model, then using nonparametric skills to model the conditional covariance matrix of the standardized errors, incorporating multiplicatively both parametric and nonparametric estimators of the conditional covariance matrix together. For every parametric MV-GARCH model, we could construct a corresponding SM-GARCH model. In both Monte Carlo simulation and empirical applications in stock indexes and foreign exchange rates, our SM-GARCH models outperform the corresponding parametric MV-GARCH models in terms of loss function (including mean absolute value of conditional correlation, mean squared error of conditional covariance matrix and Value-at-Risk (VaR) loss of the portfolio) and the p-value of the dynamic quantile test based on VaR and hit.