Empirical process of the squared residuals of an ARCH sequence

• 成果类型: Article
• 署名作者: Horváth, L; Kokoszka, P; Teyssière, G
• 署名单位: Utah System of Higher Education; University of Utah; European Commission Joint Research Centre; EC JRC ISPRA Site; University of Liverpool
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2001
• 页码: 445-469
• 关键词: WEAK-CONVERGENCE; parameters

摘要

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.