A Fourier analysis of extreme events

Thomas Mikosch, Yuwei Zhao

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

The extremogram is an asymptotic correlogram for extreme events constructed from a regularly varying stationary sequence. In this paper, we define a frequency domain analog of the correlogram: a periodogram generated from a suitable sequence of indicator functions of rare events. We derive basic properties of the periodogram such as the asymptotic independence at the Fourier frequencies and use this property to show that weighted versions of the periodogram are consistent estimators of a spectral density derived from the extremogram.

Original languageEnglish
Pages (from-to)803-845
Number of pages43
JournalBernoulli
Volume20
Issue number2
DOIs
Publication statusPublished - May 2014
Externally publishedYes

Keywords

  • ARMA
  • Asymptotic theory
  • Extremogram
  • GARCH
  • Multivariatiate regular variation
  • Periodogram
  • Spectral density
  • Stationary sequence
  • Stochastic volatility process
  • Strong mixing

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