Effect of coarse-graining on detrended fluctuation analysis

TL;DR

This study investigates how coarse-graining, a common data discretization process, impacts the accuracy of detrended fluctuation analysis (DFA) in estimating scaling exponents across various types of correlated noise.

Contribution

It demonstrates the effects of coarse-graining on DFA scaling exponent estimates and identifies conditions under which reliable estimation is possible.

Findings

Coarse-graining can significantly alter DFA scaling exponents.

Reliable estimation is possible at low levels of coarse-graining.

The number of clusters needed varies with data correlation properties.

Abstract

Several studies have investigated the scaling behavior in naturally occurring biological and physical processes using techniques such as detrended fluctuation analysis (DFA). Data acquisition is an inherent part of these studies and maps the continuous process into digital data. The resulting digital data is discretized in amplitude and time, and shall be referred to as coarse-grained realization in the present study. Since coarse-graining precedes scaling exponent analysis, it is important to understand its effects on scaling exponent estimators such as DFA. In this brief communication, k-means clustering is used to generate coarse-grained realizations of data sets with different correlation properties, namely: anti-correlated noise, long-range correlated noise and uncorrelated noise. It is shown that the coarse-graining can significantly affect the scaling exponent estimates. It is also shown that scaling exponent can be reliably estimated even at low levels of coarse-graining and the number of the clusters required varies across the data sets with different correlation properties.