Parameters estimator of GARCH(1, 1) process with heavy tailed errors

Abstract

This paper studies a modification of quasi-maximum likelihood estimator for GARCH (1, 1) process with the errors, whose squares have regularly varying tail probabilities with the exponent α, α >; 0. We showed that, this estimator is unbiased and asymptotically normal with standard convergence rate of n1/2 regardless of whether the errors are heavy-tailed.