2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/167153We consider a time series $X=\{X_k, k\in\mathbb{Z}\}$ with memory parameter $d\in\mathbb{R}$. This time series is either stationary or can be made stationary after differencing a finite number of times. We study the "Local Whittle Wavelet Estimator" of the memory parameter $d$. This is a wavelet-based semiparametric pseudo-likelihood maximum method estimator. The estimator may depend on a given finite range of scales or on a range which becomes infinite with the sample size. We show that the estimator is consistent and rate optimal if $X$ is a linear process and is asymptotically normal if $X$ is Gaussian.Statistics Theory62M15, 62M10, 62G05 (Primary); 62G20, 60G18 (Secondary)text