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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 propriLetLes asymptotiques dfun test de score traitant simultanLement des hypoth`eses portant sur des fonctions moyennes et variances conditionnelles dans une classe assez gLenLerale de mod`eles hLetLeroscLedastiques non linLeaires de sLeries chronologiques. La suite des alternatives locales considLerLee est paramLetrique portant sur les param`etres intervenant dans les fonctions moyennes et variances du mod`ele. Nous Letablissons dfabord la normalitLe locale asymptotique (LAN) du mod`ele. En se basant sur ce rLesultat la loi limite de la statistique du test proposLee a LetLe obtenue sous lfhypoth`ese nulle et aussi sous des alternatives locales en prLesence ou non des param`etres de nuisance. Key words : ARCH processes; Ergodic processes; LAN; Local power; Nonlinear processes; Score test; Time series.

An efficient locally asymptotic parametric test in nonlinear heteroscedastic time series models