A Fourier analysis of extreme events

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.

arXiv commentPublished 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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Cited by in corpus (3)

• Of copulas, quantiles, ranks and spectra: An $L_1$-approach to spectral analysis
• The integrated periodogram of a dependent extremal event sequence
• Whittle estimation based on the extremal spectral density of a heavy-tailed random field