The Annals of Statistics

Empirical process of the squared residuals of an arch sequence

Lajos Horváth and Gilles Teyssière

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Abstract

We derive the asymptotic distribution of the sequential empirical process of the squared residuals of an ARCH(p) sequence. Unlike the residuals of an ARMA process, these residuals do not behave in this context like asymptotically independent random variables, and the asymptotic distribution involves a term depending on the parameters of the model. We show that in certain applications, including the detection of changes in the distribution of the unobservable innovations, our result leads to asymptotically distribution free statistics.

Article information

Source
Ann. Statist., Volume 29, Number 2 (2001), 445-469.

Dates
First available in Project Euclid: 24 December 2001

Permanent link to this document
https://projecteuclid.org/euclid.aos/1009210548

Digital Object Identifier
doi:10.1214/aos/1009210548

Mathematical Reviews number (MathSciNet)
MR1863965

Zentralblatt MATH identifier
1012.62053

Subjects
Primary: 62G30: Order statistics; empirical distribution functions
Secondary: 62G20: Asymptotic properties

Keywords
ARCH model empirical process squared residuals

Citation

Horváth, Lajos; Teyssière, Gilles. Empirical process of the squared residuals of an arch sequence. Ann. Statist. 29 (2001), no. 2, 445--469. doi:10.1214/aos/1009210548. https://projecteuclid.org/euclid.aos/1009210548


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