Abstract
Abstrac t. In this paper we deal with a locally asymptotic stringent test for a general class of nonlinear time series heteroscedastic models. Based on the local asymptotic normality (LAN) property of these models, we propose a scoretyp test statistic for testing hypotheses on the parameters appearing in the mean and variance functions of the proposed statistical test with and without nuisance parameters. Its asymptotic null distribution is obtained as well as the local power of the test. Resume . Dans cet article, nous Letudions les propriLetLes asymptotiques dfun test de score traitant simultanLement des hypoth`eses portant sur des fonctions moyennes et variances conditionnelles dans une classe assez gLenLerale de mod`eles hLetLeroscLedastiques non linLeaires de sLeries chronologiques. La suite des alternatives locales considLerLee est paramLetrique portant sur les param`etres intervenant dans les fonctions moyennes et variances du mod`ele. Nous Letablissons dfabord la normalitLe locale asymptotique (LAN) du mod`ele. En se basant sur ce rLesultat la loi limite de la statistique du test proposLee a LetLe obtenue sous lfhypoth`ese nulle et aussi sous des alternatives locales en prLesence ou non des param`etres de nuisance. Key words : ARCH processes; Ergodic processes; LAN; Local power; Nonlinear processes; Score test; Time series.
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