R-estimators in GARCH models: asymptotics and applications

Abstract

Summary The quasi-maximum likelihood estimation is a commonly-used method for estimating the generalized autoregressive conditional heteroscedastic 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 generalized autoregressive conditional heteroscedastic parameters based on ranks of the residuals, called R-estimators, with the property that they are asymptotically normal under the existence of a finite $2+\delta$ moment of the errors and are highly efficient. We propose a fast algorithm for computing the R-estimators. Both real data analysis and simulations show the superior performance of the proposed estimators under the heavy-tailed and asymmetric distributions.