Abstract
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.
Citation
Peter Mansfield. Svetlozar T. Rachev. Gennady Samorodnitsky. "Long strange segments of a stochastic process." Ann. Appl. Probab. 11 (3) 878 - 921, August 2001. https://doi.org/10.1214/aoap/1015345352
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