We propose a new combined semiparametric estimator, which incorporates the parametric and nonparametric estimators of the conditional variance in a multiplicative way. We derive the asymptotic bias, variance, and normality of the combined estimator under general conditions. We show that under correct parametric specification, our estimator can do as well as the parametric estimator in terms of convergence rates; whereas under parametric mis-specification our estimator can still be consistent whereas the prametric estimators (ARCH/GARCH)are inconsistent and biased. Our semiparameteric estimator also improves over the nonparametric estimator of Ziegelman (2002) in terms of bias reduction. The superiority of our estimator is verfied by Monte Carlo simulations and empirical data analysis of stock returns.Our semiparametric analysis is then extended to study the forecasting of correlations in stock returns in a multivariate GARCH framework.

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