Statistics/Probability Theory
A locally asymptotically powerful test for nonlinear autoregressive models
Comptes Rendus. Mathématique, Volume 346 (2008) no. 11-12, pp. 671-676.

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.

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.

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Accepted:
Published online:
DOI: 10.1016/j.crma.2008.02.017
Chebana, Fateh 1; Laïb, Naâmane 2

1 Université du Québec, INRS-ETE, Québec G1K 9A9, Canada
2 L.S.T.A, Université Paris VI, 175, rue du Chevaleret, 75013 Paris, France
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Chebana, Fateh; Laïb, Naâmane. A locally asymptotically powerful test for nonlinear autoregressive models. Comptes Rendus. Mathématique, Volume 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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