An efficient locally asymptotic parametric test in nonlinear heteroscedastic time series models. (English) Zbl 1243.62115

Summary: 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 score typ 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.


62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62F03 Parametric hypothesis testing
62E20 Asymptotic distribution theory in statistics
62F05 Asymptotic properties of parametric tests
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