GMM Estimation of a Stochastic Volatility Model : A Monte Carlo Study

This paper examines the properties of alternative GMM procedures for estimation of the log-normal stochastic autoregessive volatility model through a large scale Monte Carlo study. We demonstrate that there is a fundamental trade-off between the number of moments, or information, included in the estimation, and the quality, or precision of the objective function used for estimation. Furthermore, a large sample approximation of the optimal weighting matrix is used to explore the impact of the weighting matrix in the estimation procedure and to obtain practical efficiency bounds for the given class of GMM estimators. Most importantly, we find that the best inference is obtained by including a lower number of moments in the GMM procedure than is often used in practical applications. Further, when an excessive number of moments is used, the chi-squared statistic is strongly downward biased, leading to a serious size distortion. For large samples, we make the specific recommendation of using the Newey and West (1993) procedure based on the Bartlett kernel and their specific data-dependent bandwidth