Robustness of coarse graining spectral analysis in estimating frequency and Hurst exponent from mixed time series with harmonic and fractal components

Abstract

While several methods have been developed to estimate the Hurst exponent H for self-affine signals, they are not sufficiently accurate when the signal has a large harmonic component. Similarly, the frequency of harmonic components cannot be estimated accurately from signals which have an underlying power-law spectrum. Coarse graining spectral analysis (CGSA) has been suggested to be capable of separating random fractals from harmonic components. In this paper, we assess the robustness and effectiveness of the CGSA method and find that it is best suited for separating harmonic and fractal components from mixed time series with low-frequency harmonics and long-term positive correlations.