Problems of Estimating Fractal Dimension by Higuchi and DFA Methods for Signals That Are a Combination of Fractal and Oscillations

Stochastic fractals of the 1/f noise type are an important manifestation of the brain’s electrical activity and other real-world complex systems. Fractal complexity can be successfully estimated by methods such as the Higuchi method and detrended fluctuation analysis (DFA). In this study, we show that if, as with the EEG, the signal is a combination of fractal and oscillation, the estimates of fractal characteristics will be inaccurate. On our test data, DFA overestimated the fractal dimension, while the Higuchi method led to underestimation in the presence of high-amplitude, densely sampled oscillations.