Higher-order Wavelet Analysis

Calculates wavelet-based bicoherence and preforms various statistical significance tests

The code performs wavelet-based higher-order spectral analysis to determine if a time series contains quadratically interacting frequency components. In particular, the code does the following:
1) Computes the wavelet-based bicoherence spectrum and performs a pointwise significance test to determine if the bicoherence at various points are statistically significant
2) Computes local wavelet-based autobicoherence and biphase to measure the degree of nonlinear interaction among three frequency components as a function of time and to determine how the nonlinear interaction influenced the cycle geometry of the time series.
3) Calculates the statistical significance of local autobicoherence against a red-noise background using Monte Carlo methods
4) Computes the diagonal slice of the full bicoherence spectrum and computes confidence intervals for the bicoherence estimates.
The code adopts and requires code written by A. Grinsted available at http://noc.ac.uk/using-science/crosswavelet-wavelet-coherence.
Useful References

Elsayed, M. A. K.: Wavelet bicoherence analysis of wind–wave interaction, Ocean Eng., 33,
458–470, 2006.
Schulte, J. A.: Wavelet analysis for non-stationary, non-linear time series, Nonlin. Processes Geophys. Discuss., 2, 1705-1737, doi:10.5194/npgd-2-1705-2015, 2015.