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A peaks over threshold model for change-point detection by wavelets
- Raimondo, M (author)
-
- Tajvidi, Nader (author)
- Lund University,Lunds universitet,Finansiell matematik,Forskargrupper vid Lunds universitet,Matematisk statistik,Matematikcentrum,Institutioner vid LTH,Lunds Tekniska Högskola,Financial Mathematics Group,Lund University Research Groups,Mathematical Statistics,Centre for Mathematical Sciences,Departments at LTH,Faculty of Engineering, LTH
- (creator_code:org_t)
- 2004
- 2004
- English.
- In: Statistica Sinica. - 1017-0405. ; 14:2, s. 395-412
- Journal article (peer-reviewed)
Abstract
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- 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.
Subject headings
- NATURVETENSKAP -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Probability Theory and Statistics (hsv//eng)
Keyword
- peaks over threshold
- nonparametric regression
- change point
- general Pareto distribution
- tail exponent wavelets
Publication and Content Type
- art (subject category)
- ref (subject category)
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