During my phd-studies I developed a theory for the direct problem of continuous wavelet synthesis including a priori wavelet spectral measures. Based on this framework I studied the inverse problem of estimating wavelet spectra and significance testing. This lead to many new results. Consequently, these pages need a thorough revision. So far, please refer to my phd-thesis or a recently published paper:

What Can We Learn from Climate Data? Methods for Fluctuation, Time/Scale and Phase Analysis, PhD Thesis, University of Potsdam, 2006, pdf, 3950 kB

D. Maraun, J. Kurths and M. Holschneider: Nonstationary Gaussian Processes in Wavelet Domain: Synthesis, Estimation and Significance Testing. Phys. Rev. E 75, 016707, 2007