Comparison of daubechies wavelets for hurst parameter estimation

摘要

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