A peaks over threshold model for change-point detection by wavelets
Raimondo, M and Tajvidi, Nader LU
(2004)
In Statistica Sinica
14(2).
p.395-412
- Abstract
- Newly available wavelet bases on multi-resolution analysis have exciting implications for detection of change-points. By checking the absolute value of wavelet coefficients one call detect discontinuities in ail otherwise smooth curve even in the presence of additive noise. In this paper, we combine wavelet methods and extreme value theory to test the presence of ail arbitrary number of discontinuities in an unknown function observed with noise. Our approach is based on a Peaks Over Threshold modelling of noisy wavelet transforms. Particular features of our method include the estimation of the extreme value index in the tail of the noise distribution. The critical region of our test is, derived using a Generalised Pareto Distribution... (More)
- Newly available wavelet bases on multi-resolution analysis have exciting implications for detection of change-points. By checking the absolute value of wavelet coefficients one call detect discontinuities in ail otherwise smooth curve even in the presence of additive noise. In this paper, we combine wavelet methods and extreme value theory to test the presence of ail arbitrary number of discontinuities in an unknown function observed with noise. Our approach is based on a Peaks Over Threshold modelling of noisy wavelet transforms. Particular features of our method include the estimation of the extreme value index in the tail of the noise distribution. The critical region of our test is, derived using a Generalised Pareto Distribution approximation to normalised sums. Asymptotic results show that our method is powerful in a wide range of medium size wavelet frequencies. We compare our test with competing approaches on simulated examples and illustrate the method on Dow-Jones data. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/279255
- author
- Raimondo, M
and Tajvidi, Nader
LU
- organization
- publishing date
- 2004
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- peaks over threshold, nonparametric regression, change point, general Pareto distribution, tail exponent wavelets
- in
- Statistica Sinica
- volume
- 14
- issue
- 2
- pages
- 395 - 412
- publisher
- Institute of Statistical Science, Academia Sinica
- external identifiers
-
- wos:000221173200004
- scopus:3142780578
- ISSN
- 1017-0405
- language
- English
- LU publication?
- yes
- id
- 2f24ffd5-c0b0-4ea2-aaab-12b5764c0c3f (old id 279255)
- alternative location
- http://www3.stat.sinica.edu.tw/statistica/
- date added to LUP
- 2016-04-01 16:56:08
- date last changed
- 2022-04-15 08:04:36
@article{2f24ffd5-c0b0-4ea2-aaab-12b5764c0c3f,
abstract = {{Newly available wavelet bases on multi-resolution analysis have exciting implications for detection of change-points. By checking the absolute value of wavelet coefficients one call detect discontinuities in ail otherwise smooth curve even in the presence of additive noise. In this paper, we combine wavelet methods and extreme value theory to test the presence of ail arbitrary number of discontinuities in an unknown function observed with noise. Our approach is based on a Peaks Over Threshold modelling of noisy wavelet transforms. Particular features of our method include the estimation of the extreme value index in the tail of the noise distribution. The critical region of our test is, derived using a Generalised Pareto Distribution approximation to normalised sums. Asymptotic results show that our method is powerful in a wide range of medium size wavelet frequencies. We compare our test with competing approaches on simulated examples and illustrate the method on Dow-Jones data.}},
author = {{Raimondo, M and Tajvidi, Nader}},
issn = {{1017-0405}},
keywords = {{peaks over threshold; nonparametric regression; change point; general Pareto distribution; tail exponent wavelets}},
language = {{eng}},
number = {{2}},
pages = {{395--412}},
publisher = {{Institute of Statistical Science, Academia Sinica}},
series = {{Statistica Sinica}},
title = {{A peaks over threshold model for change-point detection by wavelets}},
url = {{http://www3.stat.sinica.edu.tw/statistica/}},
volume = {{14}},
year = {{2004}},
}