Robust estimation and inference for heavy tailed GARCH

TL;DR

This paper introduces two robust estimators for heavy-tailed GARCH models that improve parameter estimation accuracy and inference in the presence of heavy-tailed errors, outperforming existing methods in simulations and real data applications.

Contribution

The paper develops novel tail-trimmed and transformed error estimators for GARCH models, ensuring identification, asymptotic normality, and robust inference under heavy tails.

Findings

Our estimators outperform existing methods in simulation studies.

The tail-trimmed QML estimator provides more accurate parameter estimates.

Application to financial data demonstrates practical effectiveness.

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.