Dependence Structure of Random Wavelet Coefficients in Terms of Cumulants
Philippe Naveau, Peter J. Brockwell, Doug Nychka · Defense Technical Information Center (DTIC) · 2000
When the Gaussian assumption for a times series no longer holds, second order moment properties such as the covariance and the spectrum are not necessarily sufficient to describe the dependence structure. Although wavelet models have been proposed to de-correlate the signal, this strategy must be reexamined when applied to non-Gaussian processes. The process of interest is a continuous parameter, mean-squared continuous real-valued process that is not necessarily Gaussian or linear. To study the departures from linearity and Gaussianity, we consider joint cumulants, which are linear combinations of higher order moments, and their associated spectra. A specific objective is to obtain new expressions for cumulants of the random discrete wavelet coefficients instead of the second order moments, and to study their higher order polyspectra. Conditions on the polyspectrum to give null wavelet cumulants within and across wavelet coefficient levels are derived. Expressions of the original cumulants as a function of the wavelets cumulants are also given.