Inference for unstable long-memory processes with applications to fractional unit root autoregressions

• 成果类型: Article
• 署名作者: Chan, NH; Terrin, N
• 署名单位: Carnegie Mellon University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176324318
• 发表日期: 1995
• 页码: 1662-1683
• 关键词: time-series

摘要

An autoregressive time series is said to be unstable if all of its characteristic roots lie on or outside the unit circle, with at least one on the unit circle. This paper aims at developing asymptotic inferential schemes for an unstable autoregressive model generated by long-memory innovations. This setting allows both nonstationarity and long-memory behavior in the modeling of low-frequency phenomena. In developing these procedures, a novel weak convergence result for a sequence of long-memory random variables to a stochastic integral of fractional Brownian motions is established. Results of this paper can be used to test for unit roots in a fractional AR model.