Distribution free goodness-of-fit tests for linear processes

• 成果类型: Article
• 署名作者: Delgado, MA; Hidalgo, J; Velasco, C
• 署名单位: Universidad Carlos III de Madrid; University of London; London School Economics & Political Science
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053605000000606
• 发表日期: 2005
• 页码: 2568-2609
• 关键词: long-range dependence; time-series models; LOG-PERIODOGRAM REGRESSION; spectral density; cramer-vonmises; checks; statistics; components

摘要

This article proposes a class of goodness-of-fit tests for the autocorrelation function of a time series process, including those exhibiting long-range dependence. Test statistics for composite hypotheses are functionals of a (approximated) martingale transformation of the Bartlett T-p-process with estimated parameters, which converges in distribution to the standard Brownian motion under the null hypothesis. We discuss tests of different natures such as omnibus, directional and Portmanteau-type tests. A Monte Carlo study illustrates the performance of the different tests in practice.