Robust Estimation and Inference for Heavy Tailed Nonlinear GARCH

We develop new tail-trimmed QML estimators for nonlinear GARCH models with possibly heavy tailed errors. Tail-trimming allows both identification of the true parameter and asymptotic normality. In heavy tailed cases the rate of convergence is below but arbitrarily close to root-n, the highest possible amongst M-estimators for GARCH with errors that have an infinite fourth moment, and faster than QML. We present a consistent estimator of the covariance matrix that permits classic inference without knowledge of the rate of convergence. Finally, a simulation study shows our estimators trump existing ones for sharpness and approximate normality, and we apply them to financial returns data