A Fourier analysis of extreme events
Statistics Theory
2014-03-13 v1 Statistics Theory
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.
Keywords
Cite
@article{arxiv.1403.2899,
title = {A Fourier analysis of extreme events},
author = {Thomas Mikosch and Yuwei Zhao},
journal= {arXiv preprint arXiv:1403.2899},
year = {2014}
}
Comments
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)