The Annals of Applied Probability

Long strange segments of a stochastic process

Peter Mansfield, Svetlozar T. Rachev, and Gennady Samorodnitsky

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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.

Article information

Ann. Appl. Probab. Volume 11, Number 3 (2001), 878-921.

First available in Project Euclid: 5 March 2002

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Zentralblatt MATH identifier

Primary: 60G10: Stationary processes 60F15: Strong theorems
Secondary: 60G70: Extreme value theory; extremal processes

Long-range dependence stationary process large deviations heavy tails infinite moving average maxima regular variation extreme value distribution applications in finance insurance telecommunications


Mansfield, Peter; Rachev, Svetlozar T.; Samorodnitsky, Gennady. Long strange segments of a stochastic process. Ann. Appl. Probab. 11 (2001), no. 3, 878--921. doi:10.1214/aoap/1015345352.

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