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

Abstract

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 scoretype 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.