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


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.


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Peter Mansfield. Svetlozar T. Rachev. Gennady Samorodnitsky. "Long strange segments of a stochastic process." Ann. Appl. Probab. 11 (3) 878 - 921, August 2001.


Published: August 2001
First available in Project Euclid: 5 March 2002

zbMATH: 1052.60025
MathSciNet: MR1865027
Digital Object Identifier: 10.1214/aoap/1015345352

Primary: 60F15 , 60G10
Secondary: 60G70

Keywords: applications in finance , extreme value distribution , heavy tails , infinite moving average , insurance , large deviations , long-range dependence , Maxima , regular variation , stationary process , telecommunications

Rights: Copyright © 2001 Institute of Mathematical Statistics


Vol.11 • No. 3 • August 2001
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