Robust Estimation of the Scaling Exponent in Detrended Fluctuation Analysis of Beat Rate Variability

Abstract

Detrended fluctuation analysis is a popular method for studying fractal scaling properties in time series. The method has been successfully employed in studying heart rate variability and discovering distinct scaling properties in<br/>different pathological conditions. Traditionally the analysis has been performed by extracting two scaling exponents from linear fits, for short- and long-range correlations respectively. The extent of these ranges is subjective<br/>and the linear two-range model potentially disregards additional information present in the data. <br/><br/>Here we present a method based on the Kalman smoother for obtaining a whole spectrum of scaling exponents as a function of the scale. Additionally, we present an optimization scheme to obtain data-adaptive segmentation of<br/>the fluctuation function into approximately linear regimes.<br/>The methods are parameter-free and resistant to statistical<br/>noise in the fluctutation function.<br/>We employ the methods in the analysis of the heart rate<br/>variability of patients with different heart conditions. The<br/>methods enhance the classification of these conditions, revealing more complex structure in the scaling exponents beyond the two-range model.<br/>