Arbeitspapier

On adaptive estimation in nonstationary ARMA models with GARCH errors

This paper considers adaptive estimation in nonstationary autoregressive moving average models with the noise sequence satisfying a generalised 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. Adaptivity is discussed and it is found that the parameters in the model are generally not adaptively estimable if the density of the rescaled error is asymmetric. 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 reparameterisation of the GARCH process.

Sprache
Englisch

Erschienen in
Series: ISER Discussion Paper ; No. 548

Klassifikation
Wirtschaft
Thema
Adaptive estimation
Efficient estimation
Nonstationary ARMA-GARCH models
Kernel estimators
Limiting distribution
Locally asymptotic quadratic
Log-likelihood ratio
Schätztheorie
ARCH-Modell
Theorie

Ereignis
Geistige Schöpfung
(wer)
Ling, Shiqing
MacAleer, Michael
Ereignis
Veröffentlichung
(wer)
Osaka University, Institute of Social and Economic Research (ISER)
(wo)
Osaka
(wann)
2001

Handle
Letzte Aktualisierung
10.03.2025, 11:42 MEZ

Datenpartner

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Objekttyp

  • Arbeitspapier

Beteiligte

  • Ling, Shiqing
  • MacAleer, Michael
  • Osaka University, Institute of Social and Economic Research (ISER)

Entstanden

  • 2001

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