On Estimation of Hurst Scaling Exponent and Fractal Behavior through Discrete Wavelets

We study and compare the self-similar properties of the fluctuations, as extracted through wavelet coefficients and a recently developed approach, based on discrete wavelets, which relies on the local trends extracted through the approximation coefficients. The analysis is carried out on a variety of physical data sets, as well as Gaussian white noise and binomial multi-fractal model time series. It is found that wavelets, designed to extract local polynomial trends for application to non-stationary data sets, can introduce significant variations both in small and large fluctuations, in the domain of high-pass wavelet coefficients. Hence, although the fluctuation functions based on wavelet coefficients and the other approach find the Hurst scaling exponents accurately, they differ in their estimation of the higher order moments required for finding the multifractality of the data sets. The latter approach gives more accurate result