We suggest a new approach to wavelet threshold estimation of spectral densities of stationary time series. It is well known that choosing appropriate thresholds to smooth the periodogram is difficult because non-parametric spectral estimation suffers from problems similar to curve estimation...

Nonparametric methods for the estimation of the Levy density of a Levy process X are developed. Estimators that can be writtenin terms of the "jumps" of X are introduced, and so are discrete-data based approximations. A model selection approach made up oftwo steps is investigated. The first step...