R-estimators in GARCH models; asymptotics, applications and bootstrapping

TL;DR

This paper introduces R-estimators for GARCH models that are robust to outliers, require only second moments for asymptotic normality, and outperform traditional methods in simulations and real data.

Contribution

It proposes a new class of rank-based GARCH estimators with improved robustness and efficiency, along with fast algorithms and bootstrap methods for practical application.

Findings

R-estimators are asymptotically normal under weaker moment conditions.

They outperform quasi-maximum likelihood estimators in simulations.

Bootstrap methods provide accurate finite-sample distributions.

Abstract

The quasi-maximum likelihood estimation is a commonly-used method for estimating GARCH parameters. However, such estimators are sensitive to outliers and their asymptotic normality is proved under the finite fourth moment assumption on the underlying error distribution. In this paper, we propose a novel class of estimators of the GARCH parameters based on ranks, called R-estimators, with the property that they are asymptotic normal under the existence of a more than second moment of the errors and are highly efficient. We also consider the weighted bootstrap approximation of the finite sample distributions of the R-estimators. We propose fast algorithms for computing the R-estimators and their bootstrap replicates. Both real data analysis and simulations show the superior performance of the proposed estimators under the normal and heavy-tailed distributions. Our extensive simulations also reveal excellent coverage rates of the weighted bootstrap approximations. In addition, we discuss empirical and simulation results of the R-estimators for the higher order GARCH models such as the GARCH~($2, 1$) and asymmetric models such as the GJR model.