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Asymptotic properties in ARCH(p)-time series

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  • Fuxia Cheng

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].

Suggested Citation

  • Fuxia Cheng, 2008. "Asymptotic properties in ARCH(p)-time series," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(1), pages 47-60.
    • Handle: RePEc:taf:gnstxx:v:20:y:2008:i:1:p:47-60
    DOI: 10.1080/10485250701830139
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    Cited by:

    1. Hira Koul & Nao Mimoto, 2012. "A goodness-of-fit test for GARCH innovation density," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(1), pages 127-149, January.

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