Theory

We have written a paper describing the theory behind cross wavelet and wavelet coherence. It starts from the basics of the Continuous Wavelet Transform and builds from there. "Application of the cross wavelet transform and wavelet coherence to geophysical time series."

We have also written a FAQ which has some very good information also.

We also highly recommend the paper by Torrence and Compo, "A practical guide to wavelet analysis", if you are completely new to wavelet analysis (See Links).

References

Grinsted, A., S. Jevrejeva, J. Moore, "Application of the cross wavelet transform and wavelet coherence to geophysical time series." submitted to a special issue of Nonlinear Proc. Geophys., 'Nonlinear analysis of multivariate geoscientific data - advanced methods, theory and application', 2004 [pdf]

Jevrejeva, S., J. C. Moore, and A. Grinsted, Influence of the Arctic Oscillation and El Ninő-Southern Oscillation (ENSO) on ice conditions in the Baltic Sea: The wavelet approach, J. Geophys. Res., 108(D21), 4677, doi:10.1029/2003JD003417, 2003. [pdf]

Torrence, C., and G.P. Compo, A practical guide to wavelet analysis, Bull. Am. Meteorol. Soc., 79, 61-78, 1998.

Torrence, C., and P. Webster, Interdecadal Changes in the ESNO-Monsoon System, J.Clim., 12, 2679-2690, 1999.