examples of processes falling into this model. In Section \[sec:3\] we define our estimators based on wavelet analysis for which we briefly recall the wavelet set-up. We define the local scalogram which is at the heart of our wavelet based estimators. We also prepare our technique of stationary approximation by defining what we call the approximating stationary *tangent process* and its wavelet spectrum, the *local wavelet spectrum*, as well as the pseudo-estimator *tangent scalogram*. We finish this section by discussing a series of smoothing weights, one- and two-sided kernels, which fulfill our given assumptions. The asymptotic properties of our proposed estimators are stated in the following Section \[sec:4\]. We derive a mean-square approximation of the local scalogram through the tangent scalogram (Proposition \[prop:local-scalogram\]), followed by a control of the mean square error of the scalogram as an estimator of the local wavelet spectrum (Theorem \[theo:rate-param-scalo\]) and a CLT for the tangent scalogram (Theorem \[thm:clt-tang-scal\]), which finally allows us to derive a CLT for the local scalogram (Corollary \[cor:clt-local-scalogram\]). The results on the asymptotic behavior of the estimator of $d(u)$ are then obtained: Corollary \[cor:rate-param-est\] provides the rate of convergence and Theorem \[theo:clt-param-est\] the asymptotic normality. We pursue the paper by 