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Various methods for estimating the self-similarity parameter and/or the intensity of long-range dependence in a time series are available. Some are more reliable than others. To discover the ones that work best, we apply the different methods to simulated sequences of fractional Gaussian noise and fractional ARIMA (0, d, 0). We also provide here a theoretical justification for the method of residuals of regression.
Taqqu et al. (Fri,) studied this question.