Robust Estimates for GARCH Models

In this paper we present two robust estimates for GARCH(p,q) models. The first is defined by the minimization of a conveniently modified likelihood and the second is similarly defined, but includes an additional mechanism for restricting the propagation of the effect of one outlier on the next estimated conditional variances. We study the asymptotic properties of our estimates proving consistency and asymptotic normality . A Monte Carlo study shows that the quasi maximum likelihood estimate practically collapses when there is a small percentage of outlier contamination, while the proposed robust estimates perform much better. This Monte Carlo study also includes two other robust estimates : a maximum likelihood estimate based on a Student distribution and the least absolute deviation estimate proposed by Peng and Yao. Moreover, we consider several real examples with financial data that illustrate the behavior of these estimates. Classification code: C22