Robust Estimation for ARCH Models

Abstract

This article introduces the class of the constrained M-estimators for ARCH models. The new estimators are defined based on the minimization of a bounded function of the squared residuals standardized by a robust scale. Their robustness and efficiency properties are derived. Using Monte Carlo experiments, it is shown that under small percentages of contaminations the robust estimates are still able to capture the dynamics of the process. The robust procedure is used to estimate the volatility of four Brazilian financial series.