Robust Estimation and Inference for Heavy Tailed GARCH

43 Pages Posted: 22 Oct 2013 Last revised: 18 Feb 2014

See all articles by Jonathan B. Hill

Jonathan B. Hill

University of North Carolina (UNC) at Chapel Hill – Department of Economics

Date Written: February 18, 2014

Abstract

We develop two new estimators for a general class of stationary GARCH models with possibly heavy tailed asymmetrically distributed errors, covering processes with symmetric and asymmetric feedback like GARCH, Asymmetric GARCH, VGARCH and Quadratic GARCH. The first estimator arises from negligibly trimming QML criterion equations according to error extremes. The second imbeds negligibly transformed errors into QML score equations for a Method of Moments estimator. In this case we exploit a sub-class of redescending transforms that includes tail-trimming and functions popular in the robust estimation literature, and we re-center the transformed errors to minimize small sample bias. The negligible transforms allow both identification of the true parameter and asymptotic normality. We present a consistent estimator of the covariance matrix that permits classic inference without knowledge of the rate of convergence. A simulation study shows both of our estimators trump existing ones for sharpness and approximate normality including QML, Log-LAD, and two types of non-Gaussian QML (Laplace and Power-Law). Finally, we apply the tail-trimmed QML estimator to financial data.

Suggested Citation

Hill, Jonathan B., Robust Estimation and Inference for Heavy Tailed GARCH (February 18, 2014). Available at SSRN: https://ssrn.com/abstract=2343156 or http://dx.doi.org/10.2139/ssrn.2343156

Jonathan B. Hill (Contact Author)

University of North Carolina (UNC) at Chapel Hill – Department of Economics ( email )

102 Ridge Road
Chapel Hill, NC NC 27514
United States