Asymptotic properties in ARCH(p)-time series

Fuxia Cheng

Journal of Nonparametric Statistics, 2008, vol. 20, issue 1, 47-60

Abstract: In this paper we consider the asymptotic distributions of the innovation density estimators in ARCH(p)-time series. We first obtain the asymptotic normality of the innovation density estimator at a fixed point. Globally, we show that the asymptotic distribution of the maximum of a suitably normalized deviation of the innovation density estimator from the expectation of the kernel innovation density (based on the true innovation) is the same as in the case of the one sample set up, which was given by Bickel and Rosenblatt [P.J. Bickel and M. Rosenblatt, On some global measures of the deviations of density function estimators, Ann. Statist. 6 (1973), pp. 1071–1095].

Date: 2008
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DOI: 10.1080/10485250701830139

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