A Fourier analysis of extreme events

TY - JOUR

T1 - A Fourier analysis of extreme events

AU - Mikosch, Thomas Valentin

AU - Zhao, Yuwei

PY - 2014/5

Y1 - 2014/5

N2 - 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.

AB - 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.

U2 - 10.3150/13-BEJ507

DO - 10.3150/13-BEJ507

M3 - Journal article

SN - 1350-7265

VL - 20

SP - 803

EP - 845

JO - Bernoulli

JF - Bernoulli

IS - 2

ER -