Combined Estimator of Time Series Conditional Heteroskedasticity∗

We propose a new combined estimator, called semiparametric estimator, which incorporates the parametric and nonparametric estimators of the conditional variance in a multiplicative way. We derive bias, variance, and asymptotic normality of the combined estimator. Semiparametric estimators are found to be superior to parametric and nonparametric estimators, both in simulation and empirical analysis (S&P500 index return). We find that semiparametric models capture residual asymmetry in the conditional variance ignored by the corresponding symmetric and asymmetric parametric models. Semiparametric model is found to be superior to other models in a forecast evaluation based on VaR related loss function.