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.