Long strange segments of a stochastic process

• 成果类型: Article
• 署名作者: Mansfield, P; Rachev, ST; Samorodnitsky, G
• 署名单位: University of Tasmania; Cornell University; Cornell University; Cornell University; Helmholtz Association; Karlsruhe Institute of Technology
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 2001
• 页码: 878-921
• 关键词: range dependence; noises

摘要

We study long strange intervals in a linear stationary stochastic process with regularly varying tails. It turns out that the length of the longest strange interval grows, as a function of the sample size, at different rates in different parts of the parameter space. We argue that this phenomenon may be viewed in a fruitful way as a phase transition between short- and long-range dependence, We prove a limit theorem that may form a basis for statistical detection of long-range dependence.