The Annals of Statistics

Empirical process of the squared residuals of an arch sequence

Lajos Horváth and Gilles Teyssière

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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

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

First available in Project Euclid: 24 December 2001

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

ARCH model empirical process squared residuals


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.

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