 |
| Titel |
Significance tests for the wavelet power and the wavelet power spectrum |
| VerfasserIn |
Z. Ge |
| Medientyp |
Artikel
|
| Sprache |
Englisch
|
| ISSN |
0992-7689
|
| Digitales Dokument |
URL |
| Erschienen |
In: Annales Geophysicae ; 25, no. 11 ; Nr. 25, no. 11 (2007-11-29), S.2259-2269 |
| Datensatznummer |
250015939
|
| Publikation (Nr.) |
 copernicus.org/angeo-25-2259-2007.pdf |
|
|
|
|
|
| Zusammenfassung |
| Significance tests usually address the issue how to distinguish statistically significant results from those
due to pure randomness when only one sample of the population is studied. This issue is also important
when the results obtained using the wavelet analysis are to be interpreted. Torrence and Compo (1998)
is one of the earliest works that has systematically discussed this problem. Their results, however, were
based on Monte Carlo simulations, and hence, failed to unveil many interesting and
important properties of the wavelet analysis. In the present work, the sampling distributions of the wavelet
power and power spectrum of a Gaussian White Noise (GWN) were derived in a rigorous statistical framework,
through which the significance tests for these two fundamental quantities in the wavelet analysis were
established. It was found that the results given by Torrence and Compo (1998) are numerically accurate
when adjusted by a factor of the sampling period, while some of their statements require reassessment.
More importantly, the sampling distribution of the wavelet power spectrum of a GWN was found to be highly dependent
on the local covariance structure of the wavelets, a fact that makes the significance
levels intimately related to the specific wavelet family. In addition to simulated signals, the significance
tests developed in this work were demonstrated on an actual wave elevation time series observed from a
buoy on Lake Michigan. In this simple application in geophysics, we showed how proper significance tests
helped to sort out physically meaningful peaks from those created by random noise. The derivations in the
present work can be readily extended to other wavelet-based quantities or analyses using other wavelet
families. |
| |
|
| Teil von |
|
|
|
|
|
|
|
|