ROBUST ASYMPTOTIC INFERENCE IN AUTOREGRESSIVE MODELS WITH MARTINGALE DIFFERENCE ERRORS

Abstract

This paper proposes a GMM-based method for asymptotic confidence interval construction in stationary autoregressive models, which is robust to the presence of conditional heteroskedasticity of unknown form. The confidence regions are obtained by inverting the asymptotic acceptance region of the distance metric test for the continuously updated GMM (CU-GMM) estimator. Unlike the predetermined symmetric shape of the Wald confidence intervals, the shape of the proposed confidence intervals is data-driven owing an estimated sequence of nonuniform weights. It appears that the flexibility of the CU-GMM estimator in downweighting certain observations proves advantageous for confidence interval construction. This stands in contrast to some other generalized empirical likelihood estimators with appealing optimality properties such as the empirical likelihood estimator whose objective function prevents such downweighting. A Monte Carlo simulation study illustrates the excellent small-sample properties of the method for AR models with ARCH errors. The procedure is applied to study the dynamics of the federal funds rate.