On a general class of long run variance estimators

This note proposes a class of estimators for estimating the asymptotic covariance matrix of the generalized method of moments (GMM) estimator in the stationary time series models. The proposed estimator is general enough to include the traditional heteroskedasticity and autocorrelation consistent (HAC) covariance estimator and some recently developed estimators, such as the cluster covariance estimator and projection-based covariance estimator, as special cases. We also study the first order asymptotics of the Wald statistics based on the general covariance estimators when the underlying smoothing parameter is held fixed.