Bootstrapping GMM estimators for time series

This paper considers the bootstrap for the GMM estimator of overidentified linear models when autocorrelation structures of moment functions are unknown. When moment functions are uncorrelated after finite lags, Hall and Horowitz, [1996. Bootstrap critical values for tests based on generalized method of moments estimators. Econometrica 64, 891-916] showed that errors in the rejection probabilities of the bootstrap tests are o(T-1). However, this rate cannot be obtained with the HAC covariance matrix estimator since it converges at a nonparametric rate. By incorporating the HAC covariance matrix estimator in the Edgeworth expansion of the distribution, we show that the bootstrap provides asymptotic refinements when the characteristic exponent of the kernel function is greater than two.