Generalized Method of Moments with Tail Trimming

• Activity Number: 346
• Type: Contributed
• Date/Time: Tuesday, August 3, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Jonathan B. Hill* and Eric Renault+
• Companies: The University of North Carolina at Chapel Hill and The University of North Carolina at Chapel Hill
• Keywords: GMM ; tail trimmin ; robust estimation ; heavy tails ; super consistency

Abstract

We develop a Generalized Method of Moments estimator for heavy tailed data by trimming a vanishing sample portion of the normal equations. Trimming ensures the estimator is asymptotically normal for models of heavy-tailed data, and self-normalization implies we do not need to know the rate of convergence. Tail-trimming, however, ensures asymmetric models are covered; it implies super-root-n-consistency is achievable depending on regressor and error tail thickness and dependence; and it implies possibly heterogeneous convergence rates below, at or above root-n. Models covered include nonlinear autoregressions with nonlinear GARCH errors, and random volatility models like GARCH, IGARCH and asymmetric GARCH. Simulation evidence shows the new estimator dominates GMM and QML, it is approximately normal when GMM and QML are not under very heavy tails, and reveals super-root-n-consistency.