A Fourier analysis of extremal events

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

Standard

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/rapportPh.d.-afhandling

Harvard

Zhao, Y 2013, A Fourier analysis of extremal events. Department of Mathematical Sciences, Faculty of Science, University of Copenhagen. <https://soeg.kb.dk/permalink/45KBDK_KGL/1pioq0f/alma99121972740405763>

APA

Zhao, Y. (2013). A Fourier analysis of extremal events. Department of Mathematical Sciences, Faculty of Science, University of Copenhagen. https://soeg.kb.dk/permalink/45KBDK_KGL/1pioq0f/alma99121972740405763

Vancouver

Zhao Y. A Fourier analysis of extremal events. Department of Mathematical Sciences, Faculty of Science, University of Copenhagen, 2013. 135 s.

Author

Zhao, Yuwei. / A Fourier analysis of extremal events. Department of Mathematical Sciences, Faculty of Science, University of Copenhagen, 2013. 135 s.

Bibtex

@phdthesis{ce888a7bba144ac897ff184d722cc9f4,
title = "A Fourier analysis of extremal events",
abstract = "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.",
author = "Yuwei Zhao",
year = "2013",
language = "English",
isbn = "978-87-7078-982-0",
publisher = "Department of Mathematical Sciences, Faculty of Science, University of Copenhagen",

}

RIS

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