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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)
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author
organization
publishing date
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
2007-10-30 15:29:53
date last changed
2017-07-02 04:28:31
@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},
  keyword      = {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},
  volume       = {14},
  year         = {2004},
}