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| Titel |
Geometric and topological approaches to significance testing in wavelet analysis |
| VerfasserIn |
J. A. Schulte, C. Duffy, R. G. Najjar |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
2198-5634
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics Discussions ; 1, no. 2 ; Nr. 1, no. 2 (2014-08-13), S.1331-1363 |
| Datensatznummer |
250115120
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| Publikation (Nr.) |
 copernicus.org/npgd-1-1331-2014.pdf |
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| Zusammenfassung |
| Geometric and topological methods are applied to significance testing
in the wavelet domain. A geometric test was developed for assigning
significance to pointwise significance patches in local wavelet
spectra, contiguous regions of significant wavelet coefficients with
respect to some noise model. This geometric significance test was
found to produce results similar to an existing areawise significance
test, while being more computationally flexible and efficient. The
geometric significance test can be readily applied to pointwise
significance patches at various pointwise significance levels in
wavelet power and coherence spectra. A topological analysis of
pointwise significance patches determined that holes, deficits in
pointwise significance embedded in significance patches, are capable
of identifying important structures, some of which are undetected by
the geometric and areawise tests. The application of the new and
existing significance tests to ideal time series and to the time
series of the Niño 3.4 and North Atlantic Oscillation showed that
the areawise and geometric tests perform similarly in ideal and
geophysical settings, while the topological methods showed that the
Niño 3.4 time series contains numerous phase-coherent
oscillations. |
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