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

A Fourier analysis of extreme events

Thomas Mikosch and Yuwei Zhao

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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.

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

First available in Project Euclid: 28 February 2014

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


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

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