## A Fourier analysis of extremal events

Publikation: Bog/antologi/afhandling/rapportPh.d.-afhandlingForskning

• Yuwei Zhao
The extremogram is an asymptotic correlogram for extreme events constructed from a regularly varying strictly stationary sequence. Correspondingly, the spectral density generated from the extremogram is introduced as a frequency domain analog of the extremogram. Its empirical estimator is the extremal periodogram. The extremal periodogram shares numerous asymptotic properties with the periodogram of a linear process in classical time series analysis: the asymptotic distribution of the periodogram ordinates at the Fourier frequencies have a similar form and smoothed versions of the periodogram are consistent estimators of the spectral density. By proving a functional central limit theorem, the integrated extremal
periodogram can be used for constructing asymptotic tests for the hypothesis that the data come from a strictly stationary sequence with a given extremogram or extremal spectral density. A numerical method, the stationary bootstrap, can be applied to the estimation of the integrated extremal periodogram.
Originalsprog Engelsk
Forlag Department of Mathematical Sciences, Faculty of Science, University of Copenhagen 135 978-87-7078-982-0 Udgivet - 2013

ID: 91812855