[Test localement asymptotiquemt puissant pour des modèles autoregressifs nonlinéaires]
Dans cette Note, nous proposons un test localement asymptotiquement puissant pour traiter simultanément des hypothèses portant sur les fonctions moyenne et variance conditionnelles. Ceci est fait sous des conditions de stationnarité et d'érgodicité sur une classe de modèles semi-paramétriques non-linéaires que nous considérons et lorsque la loi des innovations n'est pas nécessairement spécifiée. Basé sur une version modifiée de la méthode de Le Cam, dûe à Hwang et Basawa (2001), nous établissons la normalité locale asymptotique relative aux modèles étudiés. Le résultat principal montre que la statistique du test, construite en substituant aux résidus et aux paramètres des estimateurs consistants, est asymptotiquement normale. La puissance asymptotique du test proposé est calculée et des simulations ont été effectuées pour évaluer sa performance.
We propose a locally asymptotically powerful test to simultaneously examine hypotheses relative to the parametric form of the conditional mean and the conditional variance functions in a class of nonlinear semi-parametric time series models without a specified error law. On the basis of a modified version of the Le Cam method of Hwang and Basawa (2001), we establish the local asymptotic normality relative to the model. The main result shows that the test statistic built by substituting consistent estimated residuals and parameters for the theoretical ones is asymptotically normal. Its asymptotic power is computed and the result is illustrated by some simulations.
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@article{CRMATH_2008__346_11-12_671_0,
author = {Chebana, Fateh and La{\"\i}b, Na\^amane},
title = {A locally asymptotically powerful test for nonlinear autoregressive models},
journal = {Comptes Rendus. Math\'ematique},
pages = {671--676},
publisher = {Elsevier},
volume = {346},
number = {11-12},
year = {2008},
doi = {10.1016/j.crma.2008.02.017},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2008.02.017/}
}
TY - JOUR AU - Chebana, Fateh AU - Laïb, Naâmane TI - A locally asymptotically powerful test for nonlinear autoregressive models JO - Comptes Rendus. Mathématique PY - 2008 SP - 671 EP - 676 VL - 346 IS - 11-12 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2008.02.017/ DO - 10.1016/j.crma.2008.02.017 LA - en ID - CRMATH_2008__346_11-12_671_0 ER -
%0 Journal Article %A Chebana, Fateh %A Laïb, Naâmane %T A locally asymptotically powerful test for nonlinear autoregressive models %J Comptes Rendus. Mathématique %D 2008 %P 671-676 %V 346 %N 11-12 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2008.02.017/ %R 10.1016/j.crma.2008.02.017 %G en %F CRMATH_2008__346_11-12_671_0
Chebana, Fateh; Laïb, Naâmane. A locally asymptotically powerful test for nonlinear autoregressive models. Comptes Rendus. Mathématique, Tome 346 (2008) no. 11-12, pp. 671-676. doi : 10.1016/j.crma.2008.02.017. http://www.numdam.org/articles/10.1016/j.crma.2008.02.017/
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