Gaussian estimation of parametric spectral density with unknown pole

• 成果类型: Article
• 署名作者: Giraitis, L; Hidalgo, J; Robinson, PM
• 署名单位: University of London; London School Economics & Political Science
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2001
• 页码: 987-1023
• 关键词: long-range dependence; time-series models

摘要

We consider a parametric spectral density with power-law behavior about a fractional pole at the unknown frequency omega. The case of known omega, especially omega = 0, is standard in the long memory literature. When omega is unknown, asymptotic distribution theory for estimates of parameters, including the (long) memory parameter, is significantly harder. We study a form of Gaussian estimate. We establish n-consistency of the estimate of omega, and discuss its (non-standard) limiting distributional behavior. For the remaining parameter estimates, we establish rootn-consistency and asymptotic normality.