A Fourier analysis of extremal events
Publikation: Bog/antologi/afhandling/rapport › Ph.d.-afhandling › Forskning
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A Fourier analysis of extremal events. / Zhao, Yuwei.
Department of Mathematical Sciences, Faculty of Science, University of Copenhagen, 2013. 135 s.Publikation: Bog/antologi/afhandling/rapport › Ph.d.-afhandling › Forskning
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TY - BOOK
T1 - A Fourier analysis of extremal events
AU - Zhao, Yuwei
PY - 2013
Y1 - 2013
N2 - 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 extremalperiodogram 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.
AB - 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 extremalperiodogram 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.
UR - https://soeg.kb.dk/permalink/45KBDK_KGL/1pioq0f/alma99121972740405763
M3 - Ph.D. thesis
SN - 978-87-7078-982-0
BT - A Fourier analysis of extremal events
PB - Department of Mathematical Sciences, Faculty of Science, University of Copenhagen
ER -
ID: 91812855