telecommunication (e.g. teletraffic data) but recently also in economics and in finance, e.g. for modelling (realized) volatility of exchange rate data or stocks. The literature on stationary long-memory processes is huge (see e.g. the references in the recent survey paper [@fay-mouline-roueff-taqqu-2009]), and we concentrate here on the discussion of long-range dependence resulting from a singularity of the spectral density at zero frequency - corresponding to a slow, i.e. polynomial, decay of the autocorrelation of the data. Although a lot of (earlier) work started from a parametric approach, using e.g. the celebrated ARFIMA-like models, it occurs that since the seminal work by P. Robinson (see [@robinson:1995:GSE; @robinson:1995:GPH]), the semi-parametric approach is known to be more robust against model misspecification: instead of using a parametric filter describing both the singularity of the spectral density at zero frequency and the ARMA-dynamics of the short memory part, only the singular behavior of the spectrum at zero is modelled by the long-memory parameter, $d$ say, whereas the short memory part remains completely non-parametric.

Driven by the empirical observation that the correlation structure of observed (weakly or strongly dependent) data can change over time, there is a also a growing literature on modelling departures from covariance-stationarity, 