A Fourier analysis of extreme events
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A Fourier analysis of extreme events. / Mikosch, Thomas Valentin; Zhao, Yuwei.
In: Bernoulli, Vol. 20, No. 2, 2014, p. 803-845.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - A Fourier analysis of extreme events
AU - Mikosch, Thomas Valentin
AU - Zhao, Yuwei
PY - 2014
Y1 - 2014
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
VL - 20
SP - 803
EP - 845
JO - Bernoulli
JF - Bernoulli
SN - 1350-7265
IS - 2
ER -
ID: 102654890