Cumulative Areawise Testing in Wavelet Analysis

Preforms the cumulative areawise test

The code is used to implement the cumulative areawise test on geometric pathways in the wavelet domain, where geometric pathways are a nested sequence of patches together with normalized areas. Patches are defined as contiguous regions of pointwise significance and the normalized areas are calculated by dividing the area of the patch by the square of the scale-coordinate of its centroid. The procedure can applied to pathways in wavelet power, wavelet coherence, and wavelet partial coherence spectra. Additionally, for wavelet power spectra, the procedure can be applied to wavelet spectra obtained using the Morlet, Paul, and DOG analyzing wavelets. The critical level of the test needs to be calculated using Monte Carlo methods; however, three files containing the null distributions for the Morlet, Paul, and DOG wavelets are provided and are directly loaded when the code is run. The null distributions are only valid for the default values and so different null distributions must be calculated if non-default values are used. See the demo file to learn how different null distributions are calculated.
The code is a modified version of the code written by A. Grinsted available at http://www.pol.ac.uk/home/research/waveletcoherence/ and that written by Eric K. W. Ng available at http://www.cityu.edu.hk/gcacic/wavelet/. The user should download those software packages, as they are required to run the cumulative areawise testing software. The user should also download the code written by C. Torrence and G. Compo (http://paos.colorado.edu/research/wavelets/software.html). The also requires the geometric significance testing software available on File Exchange (http://www.mathworks.com/matlabcentral/fileexchange/50110-geometric-and-topological-methods-for-significance-testing-in-wavelet-analysis)
Schulte, J. A.: Cumulative areawise testing in wavelet analysis and its application to geophysical time series, Nonlin. Processes Geophys. Discuss., 2, 1227-1273, doi:10.5194/npgd-2-1227-2015, 2015.