Open Access
August 2015 Robust estimation and inference for heavy tailed GARCH
Jonathan B. Hill
Bernoulli 21(3): 1629-1669 (August 2015). DOI: 10.3150/14-BEJ616


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.


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Jonathan B. Hill. "Robust estimation and inference for heavy tailed GARCH." Bernoulli 21 (3) 1629 - 1669, August 2015.


Received: 1 December 2012; Revised: 1 February 2014; Published: August 2015
First available in Project Euclid: 27 May 2015

zbMATH: 1319.62192
MathSciNet: MR3352056
Digital Object Identifier: 10.3150/14-BEJ616

Keywords: GARCH , heavy tails , QML , robust inference , tail trimming

Rights: Copyright © 2015 Bernoulli Society for Mathematical Statistics and Probability

Vol.21 • No. 3 • August 2015
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