Asymptotic Results for GMM Estimators of Stochastic Volatility Models

We derive closed-form expressions for the optimal weighting matrix for GMM estimation of the stochastic volatility model with AR(1) log-volatility, and for the asymptotic covariance matrix of the resulting estimator. The moment conditions considered are generated by the absolute observations (which is the standard approach in this literature) or by the log-squared observations. We use the expressions to compare the performances of GMM and other estimators that have been proposed, and to optimally select small sets of moment conditions from very large sets.