A Note on the Effect of Wavelet Choice on the Estimation of the Evolutionary Wavelet Spectrum

摘要

The locally stationary wavelet process model assumes some underlying wavelet family in order to generate the process. Analyses of such processes also assume that the same wavelet family is used to obtain unbiased estimates of the wavelet spectrum. In practice this would not typically be possible since, a priori, the underlying wavelet family is not known. This article considers the effect of wavelet choice within this setting. A particular focus is given to the estimation of the evolutionary wavelet spectrum due to its importance in many reported applications.