descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 May 2014Embargo end date: 01 Jan 2014Publisher:Bernoulli Society for Mathematical Statistics and ProbabilityJournal:Bernoulli, volume 20 (issn: 1350-7265,

Authors: Mikosch, Thomas Valentin; Zhao, Yuwei;

doi: 10.3150/13-bej507 , 10.48550/arxiv.1403.2899

arXiv: http://arxiv.org/abs/1403.2899

A Fourier analysis of extreme events

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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.

Published in at http://dx.doi.org/10.3150/13-BEJ507 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

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Keywords

GARCH, stochastic volatility process, Mathematics - Statistics Theory, Statistics Theory (math.ST), periodogram, extremogram, stationary sequence, asymptotic theory, multivariatiate regular variation, spectral density, strong mixing, FOS: Mathematics, ARMA

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