Long memory or long range dependence can be seen as a class of stationary models approaching the border of non-stationarity. Interesting insights are provided in G. Samorodnitsky's book published in 2006. In this contribution, we examine some cases where long memory models cross this border. A well known case is the extension of the long memory parameter to values larger than 0.5. We will recall the different approaches that has been proposed to do so for linear processes and also in the case of a non-linear process, the so called infinite source Poisson process. A second important example of non-stationary models is that of locally stationary processes that allow the long memory parameter to vary along time. Wavelet estimators can be adapted in this context to construct estimators of the local long memory parameter.
The main difficulty here is to cope with two opposite goals: 1) provide a local analysis 2) focus on low frequencies.
Keywords: Long memory; Semi-parametric modelling; Wavelets; Locally stationary processes
Biography: François Roueff received the M.Sc. degree from the Ecole Polytechnique in 1995 and the Ph.D. degree in signal processing from the Ecole Nationale Supérieure des Telecommunications, now known as Telecom ParisTech, in 2000.
He is currently a Professor at Telecom ParisTech, within the STA group of the LTCI lab (Institut Telecom/CNRS). His research interests include statistics, statistical signal processing and applied probability. He was recently involved in research projects on wavelet methods for estimating the long memory parameter.