Computational validation of fractal characterization by using the wavelet-based fractal analysis

Abstract

In this paper, the performance of the wavelet-based fractal analysis for fractal characterization is computationally validated. In the wavelet-based fractal analysis, the spectral exponent γ that is related to the scaling exponent α characterizing the long-range correlation is obtained from the slope of the log-variance of the wavelet coefficients versus scale graph. The wavelet-based fractal analysis is applied to a set of simulated time series associated with various scaling exponents. The scaling exponents derived from the corresponding spectral exponents of the simulated time series are examined. From the computational results with the 4th-order Daubechies wavelet bases, the wavelet-based fractal analysis is shown to be able to quantify the scaling exponents excellently and provide better performance compared to the commonly-used detrended fluctuation analysis (DFA). Overall, the average error in the estimate of the scaling exponent by using the wavelet-based fractal analysis is less than 2.50%. However, the multifractal detrended fluctuation analysis shows that the simulated time series exhibit weak multifractal characteristics.