Significance test areawise

To estimate wavelet spectra and to perform areawise significance tests, we developed a free R-package based on the package Rwave by Carmona et. al. [2]. All wavelet plots in this paper have been realized with this software. It can be downloaded from http //www.agnld.uni-potsdam.de/ maraun/wavelets... 

Fig. 12.7. (Taken from [17]) Areawise significance test performed on the example from (Fig. 12.6). Most of the spurious patches are sorted out.

Note, that on every scale a, the area is related to the corresponding measure a. We now define the significance level of the areawise test as... 

Stretch the reproducing kernel for every scale according to Eq. (12.3), choose a significance level 1 — a aw for the areawise test and the corresponding critical area Peru b, a) of the reproducing kernel. 

Figure 12.7 illustrates the areawise test based on the result of the pointwise test for a Gaussian white noise realization shown in Fig. 12.6. The areawise test is capable of identifying about 90% of the spuriously significant area from the pointwise test.

Also here, an areawise test can be performed to sort out false positive patches being artefacts from time/frequency resolved analysis. The procedure is exactly the same as for the wavelet spectrum, only the critical patchsize Pcrit b, a) has to be reestimated. Areawise significant patches denote significant common oscillations of two processes. Here, common means that two processes exhibit a rather stable phase relation on a certain scale for a certain time intervall. 

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