This paper analyzes the higher order asymptotic properties of Generalized Method of Moments (GMM) estimators for linear time series models using many lags as instruments. A data dependent moment selection method based on minimizing the approximate mean squared error is developed. In addition, a new version of the GMM estimator based on kernel weighted moment conditions is proposed. It is shown that kernel weighted GMM can reduce the asymptotic bias compared to standard GMM. Kernel weighting also helps to simplify the problem of selecting the optimal number of instruments. A feasible procedure similar to optimal bandwidth selection is proposed for the kernel weighted GMM estimator.