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.
"Empirical process of the squared residuals of an arch sequence." Ann. Statist. 29 (2) 445 - 469, April 2001. https://doi.org/10.1214/aos/1009210548