Narrow-band analysis of nonstationary processes

• 成果类型: Article
• 署名作者: Robinson, PM; Marinucci, D
• 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: 947-986
• 关键词: long-range dependence; time-series; unit-root; CONVERGENCE; estimators; inference; forms

摘要

The behavior of averaged periodograms and cross-periodograms of a broad class of nonstationary processes is studied. The processes include nonstationary ones that are fractional of any order, as well as asymptotically stationary fractional ones. The cross-periodogram can involve two nonstationary processes of possibly different orders, or a nonstationary and an asymptotically stationary one. The averaging takes place either over the whole frequency band, or over one that degenerates slowly to zero frequency as sample size increases. In some cases it is found to make no asymptotic difference, and in particular we indicate how the behavior of the mean and variance changes across the two-dimensional space of integration orders. The results employ only local-to-zero assumptions on the spectra of the underlying weakly stationary sequences. It is shown how the results can be applied in fractional cointegration with unknown integration orders.