Please use this identifier to cite or link to this item: http://hdl.handle.net/1783.1/1402

On Adaptive Estimation in Nonstationary ARMA Models with GARCH Errors

Authors Ling, S.
McAleer, M.
Issue Date 2003
Source Annals of statistics , v. 31, (2), 2003, p. 642-674
Summary This paper considers adaptive estimation in nonstationary autoregressive moving average models with the noise sequence satisfying a generalized autoregressive conditional heteroscedastic process. The locally asymptotic quadratic form of the log-likelihood ratio for the model is obtained. It is shown that the limit experiment is neither LAN nor LAMN, but is instead LABF. For the model with symmetric density of the rescaled error, a new efficiency criterion is established for a class of defined Mv-estimators. It is shown that such efficient estimators can be constructed when the density is known. Using the kernel estimator for the score function, adaptive estimators are constructed when the density of the rescaled error is symmetric, and it is shown that the adaptive procedure for the parameters in the conditional mean part uses the full sample without splitting. These estimators are demonstrated to be asymptotically efficient in the class of Mv-estimators. The paper includes the results that the stationary ARMA-GARCH model is LAN, and that the parameters in the model with symmetric density of the rescaled error are adaptively estimable after a reparameterization of the GARCH process. This paper also establishes the locally asymptotic quadratic form of the log-likelihood ratio for nonlinear time series models with ARCH-type errors.
Subjects
ISSN 0090-5364
Rights ©Institute of Mathematical Statistics 2003; the official site of the journal: http://www.imstat.org/aos/
Language English
Format Article
Access View full-text via DOI
View full-text via Scopus
View full-text via Web of Science
Find@HKUST
Files in this item:
File Description Size Format
rrea2.pdf 302168 B Adobe PDF