Cumulative Arcwise Significance of Global Wavelet Power and Global Coherence Spectra

This software performs the cumulative arcwise test to determine if peaks in global wavelet spectra are statistically significant. Traditionally, the statistical significance of global wavelet power or coherence is tested individually at each wavelet scale, so-called pointwise significance testing (Torrence and Compo, 1998). As noted by Maraun and Kurths (2007) such a pointwise approach will produce contiguous regions of pointwise significance. Moreover, the simultaneous testing of multiple hypotheses is also a deficiency of pointwise significance testing given the number of wavelet quantities to which the pointwise tests are applied. To account for the aforementioned deficiencies of pointwise testing, one can assess the statistical significance of the contiguous regions of pointwise significance. For full wavelet spectra, the contiguous regions are patches or polygons. In global wavelet spectra, the contiguous regions are pointwise significance arcs. Thus, the arcwise test assesses the statistical significance of the arcs based on their arc length. To account for how the test could be sensitive to the chosen pointwise significance level, one can track how the arc length changes as one adjusts the pointwise significance level (hence the name cumulative arcwise testing). A practical example can be found in the paper with associated link https://doi.org/10.1175/JCLI-D-17-0135.1.

This software makes use of the excellent code written by Aslak Grinsted, which can be found on file exchange (https://www.mathworks.com/matlabcentral/fileexchange/47985-cross-wavelet-and-wavelet-coherence).
Useful References
A. Grinsted, J. C. Moore, S. Jevrejeva. Application of the cross wavelet transform and wavelet
coherence to geophysical time series. Nonlinear Processes in Geophysics, European Geosciences Union
(EGU), 2004, 11 (5/6), pp.561-566. <hal-00302394

Maraun, D. and Kurths, J.: Cross wavelet analysis: significance testing and pitfalls, Nonlin. Processes Geophys., 11, 505–514, 2004.

Maraun, D., Kurths, J., and Holschneider, M.: Nonstationary Gaussian processes in wavelet domain: synthesis, estimation, and significance testing, Phys. Rev. E, 75, doi:10.1103/PhysRevE.75.016707, 2007.

Schulte, J. A., Duffy, C., and Najjar, R. G.: Geometric and topological approaches to significance testing in wavelet analysis, Nonlin. Processes Geophys., 22, 139–156, doi:10.5194/npg-22-139- 2015, 2015.

Schulte, J. A.: Cumulative areawise testing in wavelet analysis and its application to geophysical time series, Nonlin. Processes Geophys., 23, 45-57, https://doi.org/10.5194/npg-23-45-2016, 2016

Torrence, C. and Compo, G. P.: A practical guide to wavelet analysis, B. Am. Meteor. Soc., 79, 61–78, 1998.