Comparison of daubechies wavelets for hurst parameter estimation

Time scale dependence on the working nature of wavelet analysis makes it a valuable tool for Hurst parameter estimation. Similar to other wavelet-based signal processing applications, the selection of a particular wavelet type and vanishing moment in wavelet based Hurst estimation is a challenging problem. In this paper, we investigate the best Daubechies wavelet in wavelet based Hurst estimation for an exact self similar process, fractional Gaussian noise and how Daubechies vanishing moment affects the Hurst estimation accuracy. Daubechies wavelets are preferred in analysis because increasing vanishing moment does not cause excessive increase of time support of Daubechies wavelets. Thus, limited time support of wavelets reduces the border effects. Results show that Daubechies wavelets with one vanishing moment (Daubechies 1) gives the best estimation result for short range dependent fractional Gaussian noise. Daubechies 2 is the best preference for long range dependent fractional Gaussian noise.