We propose a class of estimators for the parameters of a GARCH(p,q) sequence. We show that our estimators are consistent and asymptotically normal under mild conditions. The quasi-maximum likelihood and the likelihood estimators are discussed in detail. We show that the maximum likelihood estimator is optimal. If the tail of the distribution of the innovations is polynomial, even a quasi-maximum likelihood estimator based on exponential density performs better than the standard normal density-based quasi-likelihood estimator of Lee and Hansen and Lumsdaine.
Publié le : 2004-04-14
Classification:
GARCH(p, q) sequence,
quasi-maximum likelihood,
asymptotic normality,
asymptotic covariance matrix,
Fisher information number,
62F12,
62M10
@article{1083178941,
author = {Berkes, Istv\'an and Horv\'ath, Lajos},
title = {The efficiency of the estimators of the parameters in GARCH processes},
journal = {Ann. Statist.},
volume = {32},
number = {1},
year = {2004},
pages = { 633-655},
language = {en},
url = {http://dml.mathdoc.fr/item/1083178941}
}
Berkes, István; Horváth, Lajos. The efficiency of the estimators of the parameters in GARCH processes. Ann. Statist., Tome 32 (2004) no. 1, pp. 633-655. http://gdmltest.u-ga.fr/item/1083178941/