I am looking for the Hurst exponent calculation methodology. Please suggest online materials / methodology papers.
The calculation is covered on the related wikipedia page.
R has several implementations for this:
The methods covered by fArma are taken from the "Estimators for Long-Range Dependence: An Empirical Study" (Taqqu, Teverovsky, Willinger 1995).
Edit: Just to add from the M. Tibbits comment below, you can find the Hurst exponent code for Matlab offered under a BSD license. The description: