GMM Long-Run Variance Estimation via VAR Averaging

Abstract

This paper examines the heteroskedasticity and autocorrelation consistent (HAC) estimation of the long-run variance (LRV) matrix of a random vector process in a GMM estimation framework via vector autoregression (VAR) model averaging. By combining a VAR representation of GMM moments and VAR model averaging techniques, we present two new averaging-VAR-based LRV estimators: One constructs the LRV estimator based on the data-dependent weighted VAR residuals, and the other additionally combines with prewhitened kernel estimators in the spirit of Andrews and Monahan (1992). Our former proposal does not suffer from problems involving the choices of a truncation lag (bandwidth) or VAR lag length that are inherent in existing methods; the latter can be viewed as employing the VAR averaging strategy for prewhitening purposes. Theoretical justifications of the proposed methods rely on new consistency results for the averaging least-squares estimation of VAR coefficients and for the proposed LRV estimators. In extensive simulation experiments, our new averaging-VAR-based LRV estimators perform well in finite samples by offering more inference accuracy relative to existing competing estimators, with the improvement particularly prominent when combining VAR averaging with prewhitened kernel estimators. We empirically test the forward rate unbiasedness hypothesis to illustrate the utility of our methodology.