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

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
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
and the linear two-range model potentially disregards additional information present in the data.

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
the fluctuation function into approximately linear regimes.
The methods are parameter-free and resistant to statistical
noise in the fluctutation function.
We employ the methods in the analysis of the heart rate
variability of patients with different heart conditions. The
methods enhance the classification of these conditions, revealing more complex structure in the scaling exponents beyond the two-range model.