Long strange segments in a long-range-dependent moving average

Svetlozar T. Rachev, Gennady Samorodnitsky

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

We establish the rate of growth of the length of long strange intervals in an infinite moving average process whose coefficients are regularly varying at infinity. We compute the limiting distribution of the appropriately normalized length of such intervals. The rate of growth of the length of long strange intervals turns out to change dramatically once the exponent of regular variation of the coefficients becomes smaller than 1, and then the rate of growth is determined both by the exponent of regular variation of the coefficients and by the heaviness of the tail distribution of the noise variables.

Original languageEnglish
Pages (from-to)119-148
Number of pages30
JournalStochastic Processes and their Applications
Volume93
Issue number1
DOIs
StatePublished - May 2001

Keywords

  • 60F15
  • Applications in finance
  • Extreme value distribution
  • Heavy tails
  • Insurance
  • Large deviations
  • Long-range dependence
  • Moving average process
  • Primary 60G10
  • Regular variation
  • Secondary 60G70
  • Telecommunications

Fingerprint Dive into the research topics of 'Long strange segments in a long-range-dependent moving average'. Together they form a unique fingerprint.

Cite this