Bernoulli

  • Bernoulli
  • Volume 20, Number 2 (2014), 803-845.

A Fourier analysis of extreme events

Thomas Mikosch and Yuwei Zhao

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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.

Article information

Source
Bernoulli, Volume 20, Number 2 (2014), 803-845.

Dates
First available in Project Euclid: 28 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.bj/1393594007

Digital Object Identifier
doi:10.3150/13-BEJ507

Mathematical Reviews number (MathSciNet)
MR3178519

Zentralblatt MATH identifier
1321.60110

Keywords
ARMA asymptotic theory extremogram GARCH multivariatiate regular variation periodogram spectral density stationary sequence stochastic volatility process strong mixing

Citation

Mikosch, Thomas; Zhao, Yuwei. A Fourier analysis of extreme events. Bernoulli 20 (2014), no. 2, 803--845. doi:10.3150/13-BEJ507. https://projecteuclid.org/euclid.bj/1393594007


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