The efficiency of the estimators of the parameters in GARCH processes

Abstract

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.

Cited by in corpus (11)

• Global self-weighted and local quasi-maximum exponential likelihood estimators for ARMA--GARCH/IGARCH models
• Continuous invertibility and stable QML estimation of the EGARCH(1,1) model
• High moment partial sum processes of residuals in GARCH models and their applications
• Robust estimation and inference for heavy tailed GARCH
• Estimation in a class of nonlinear heteroscedastic time series models
• Weighted bootstrap in GARCH models
• Non-Gaussian Quasi Maximum Likelihood Estimation of GARCH Models
• Empirical processes of dependent random variables
• Test for parameter change in the presence of outliers: the density power divergence based approach
• R-estimators in GARCH models; asymptotics, applications and bootstrapping
• Quasi-maximum likelihood estimation of periodic GARCH processes