Long strange segments of a stochastic process

Peter Mansfield, Svetlozar T. Rachev, Gennady Samorodnitsky

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11 Scopus citations

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.

Original languageEnglish
Pages (from-to)878-921
Number of pages44
JournalAnnals of Applied Probability
Volume11
Issue number3
DOIs
StatePublished - Aug 2001

Keywords

  • Applications in finance
  • Extreme value distribution
  • Heavy tails
  • Infinite moving average
  • Insurance
  • Large deviations
  • Long-range dependence
  • Maxima
  • Regular variation
  • Stationary process
  • Telecommunications

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