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April 2001 Empirical process of the squared residuals of an arch sequence
Lajos Horváth, Gilles Teyssière
Ann. Statist. 29(2): 445-469 (April 2001). DOI: 10.1214/aos/1009210548


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.


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Lajos Horváth. Gilles Teyssière. "Empirical process of the squared residuals of an arch sequence." Ann. Statist. 29 (2) 445 - 469, April 2001.


Published: April 2001
First available in Project Euclid: 24 December 2001

zbMATH: 1012.62053
MathSciNet: MR1863965
Digital Object Identifier: 10.1214/aos/1009210548

Primary: 62G30
Secondary: 62G20

Keywords: ARCH model , empirical process , squared residuals

Rights: Copyright © 2001 Institute of Mathematical Statistics


Vol.29 • No. 2 • April 2001
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