Empirical process of the squared residuals of an arch\n\t\t\t sequence

Abstract

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