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In this paper, we study robust estimators of the memory parameter d of a(possibly) non stationary Gaussian time series with generalized spectraldensity f. This generalized spectral density is characterized by the memoryparameter d and by a function f* which specifies the short-range dependencestructure of the process. Our setting is semi-parametric since both f* and dare unknown and d is the only parameter of interest. The memory parameter d isestimated by regressing the logarithm of the estimated variance of the waveletcoefficients at different scales. The two estimators of d that we consider arebased on robust estimators of the variance of the wavelet coefficients, namelythe square of the scale estimator proposed by Rousseeuw and Croux (1993) andthe median of the square of the wavelet coefficients. We establish a CentralLimit Theorem for these robust estimators as well as for the estimator of dbased on the classical estimator of the variance proposed by Moulines, Roueffand Taqqu (2007). Some Monte-Carlo experiments are presented to illustrate ourclaims and compare the performance of the different estimators. The propertiesof the three estimators are also compared on the Nile River data and theInternet traffic packet counts data. The theoretical results and the empiricalevidence strongly suggest using the robust estimators as an alternative toestimate the memory parameter d of Gaussian time series.

Central limit theorem for the robust log-regression wavelet estimation of the memory parameter in the Gaussian semi-parametric context