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Please use this identifier to cite or link to this item: http://hdl.handle.net/1783.1/1402
Title: On adaptive estimation in nonstationary ARMA models with GARCH errors
Authors: Ling, Shi-Qing
McAleer, Michael
Keywords: Adaptive estimation
Efficient estimation
Nonstationary ARMA-GARCH models
Kernel estimators
Limiting distribution
Locally asymptotic quadratic
Log-likelihood ratio
Issue Date: Mar-2003
Citation: The annals of statistics, 2003, v. 31, no. 2, p. 642-674
Abstract: 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.
Rights: ¬©Institute of Mathematical Statistics 2003; the official site of the journal: http://www.imstat.org/aos/
URI: http://hdl.handle.net/1783.1/1402
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