Wavelet and rescaled range approach for the Hurst coefficient for short and long time series

The calculation of Hurst coefficient ( H) by different techniques is sensitive to the length of the profile and noise. Synthetic fractional Brownian motions with different values of H have been generated and the effectiveness of the techniques has been tested on these time series. H values are calculated by wavelet transform (WT), power spectrum (PS), roughness length (RL), semi-variogram (SV), and rescaled range ( R/ S) methods. On the basis of the error estimates two methods: R/ S analysis and WT are suggested for calculation of H for short/long datasets. Further, WT method is applied to geophysical data of the Bay of Bengal. The gravity, magnetic and bathymetry data indicate the self-affine nature with H=0.8, 0.8 and 0.9, respectively.