Parameters estimation of GARCH(1,1) process with regularly varying tailed errors

Abstract

In this paper, we established the consistency and asymptotic distribution of estimation of parameters for GARCH(1,1) process with the errors, whose squares have regularly varying tail probabilities with the index a, a > 0. Using a modification of Gaussian quasi-maximum likelihood estimation, we showed that, the estimation of our method is consistent, the asymptotic distribution can be normality, or stable random variable with other values of a.