Performance analysis of Hurst exponent estimators using surrogate-data and fractional lognormal noise models: Application to breathing signals from preterm infants

Abstract

Listen

Translate article

The use of the Hurst exponent (H) to quantify the fractal characteristics of biological signals and its potential to detect abnormalities has aroused, recently, the interest of many researchers. Numerous techniques to estimate H are described in the literature, yet the choice of the most performing one is not straightforward. In this paper, we proposed some tests using artificial signals from experimental data and stochastic models to evaluate the robustness of three estimation techniques. Different surrogate-data tests, including a novel method to parametrize the degree of correlation in experimental signals with H (Hurst-adjusted surrogates), were first carried out. Then, simulated signals with prescribed H were obtained from fractional Gaussian noise modified properly to follow the lognormal laws observed in empirical data. The tests were applied to examine detrended fluctuation analysis (DFA), discrete wavelet transform and least squares based on standard deviation (LSSD) methods in the particular case of inter-breath interval signals from preterm infants. Simulations showed that none of the estimators were robust for every breathing pattern (regular, erratic and periodic) and should not be applied blindly without performing the preliminary tests proposed here. The LSSD technique was the most precise in general, but DFA was more robust with highly spiked patterns.