Mr. Charfeddine

Thanks for the supplied references.

I'll take a further look into them.

Best Regards

For validating the results check the tool for Hurst exponent available in CDApro..

Sorry I am too lazy to find the right paper it is some were buried in my folder of PDFs. I googled it and found this.  Wavelet based technique will give you a very good insight in to singularities in your signal which give rise to the signals structured noise. This technique will give you more then just a Hurst exponent. If you need to I can hook you up the the best software that implements it. I am very good friends with Alain Arneodo who came up with the technique

http://www.scholarpedia.org/article/Wavelet-based_multifractal_analysis

GHE is a good algorithm. You can also check the algorithm provided in the attached paper, which is quite robust for self similar series.

Article An accurate algorithm to calculate the Hurst exponent of sel...

Dears

I'm also looking for an R package which also implements the Whittle estimator also used in Estimators for Long Range Dependence: An Empirical Study. (http://arxiv.org/pdf/0901.0762.pdf).

I'm also using the R fArma package ( https://cran.r-project.org/web/packages/fArma/fArma.pdf ) no longer implments this estimator.

For GPH and Haslett-Raftery estimators I'm using the fracDiff (https://cran.r-project.org/web/packages/fracdiff/fracdiff.pdf) package.

Best Regards.

Article The Estimation and Application of Long Memory Time Series Model

Article Space-Time Modelling with Long-Memory Dependence: Assessing ...

Mr. Smith

Thank you very much for the advice and also for the refference paper.

Would the suggested Surrorgate tests from the Wikipedia article (https://en.wikipedia.org/wiki/Surrogate_data_testing) be suitable for testing H estimators ?

BTW : Do you have an example for an "overfitted" H over a non-longe-range pestistent series ? =P 

Best Regards. 

See section 4.2 in my paper here http://arxiv.org/pdf/0807.3374v4.pdf. There are a variety of methods but I would say least squares fitting on a log-log autocorrelation and diffusion limited aggregation (DLA) are the least robust. Wavelet methods are best and the unbiased exponent estimator calculation method using logscale diagrams is given in this paper: http://perso.ens-lyon.fr/patrick.flandrin/wwbook_abry.pdf. This is better, especially if your data is nonstationary.

Hi, you may check the R package "dvfBm", which uses the discrete variation method.

As discussed in the literature, it has a robust estimation of H, by choosing the method= "Q" or "TM" in the function dvFBM.

Hope that help.