This paper studies the quasi-maximum likelihood estimator (QMLE) for the generalized autoregressive conditional heteroscedastic (GARCH) model based on the Laplace (1,1) residuals. The QMLE is proposed to the parameter vector of the GARCH model with the Laplace (1,1) firstly. Under some certain conditions, the strong consistency and asymptotic normality of QMLE are then established. In what follows, a real example with Laplace and normal distribution is analyzed to evaluate the performance of the QMLE and some comparison results on the performance are given. In the end the proofs of some theorem are presented.
@article{bwmeta1.element.doi-10_1515_math-2017-0131,
author = {Haiyan Xuan and Lixin Song and Muhammad Amin and Yongxia Shi},
title = {Quasi-maximum likelihood estimator of Laplace (1, 1) for GARCH models},
journal = {Open Mathematics},
volume = {15},
year = {2017},
pages = {1539-1548},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2017-0131}
}
Haiyan Xuan; Lixin Song; Muhammad Amin; Yongxia Shi. Quasi-maximum likelihood estimator of Laplace (1, 1) for GARCH models. Open Mathematics, Tome 15 (2017) pp. 1539-1548. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2017-0131/