---
abstract: 'There exists a wide literature on parametrically or semi-parametrically modeling strongly dependent time series using a long-memory parameter $d$, including more recent work on wavelet estimation. As a generalization of these latter approaches, in this work we allow the long-memory parameter $d$ to be varying over time. We adopt a semi-parametric approach in order to avoid fitting a time-varying parametric model, such as tvARFIMA, to the observed data. We study the asymptotic behavior of a local log-regression wavelet estimator of the time-dependent $d$. Both simulations and a real data example complete our work on providing a fairly general approach.'
address:
- 'Institut Telecom, Telecom Paris, CNRS LTCI, 46 rue Barrault, 75634 Paris Cedex 13, France'
- 'Institut de statistique, Université catholique de Louvain, Voie du Roman Pays, 20, B-1348 Louvain-la-Neuve, Belgium'
author:
- François Roueff
- Rainer von Sachs
bibliography:
- 'lrd.bib'
date: 'April 8, 2010'
title: Locally stationary long memory estimation
---

Introduction {#sec:1}
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There is a long tradition of modelling the phenomenon of long-range dependence in observed data that show a strong persistence of their correlations by long-memory processes. Such data can typically be found in the applied sciences such as hydrology, geophysics, climatology and 