Minimizing the effect of trends on detrended fluctuation analysis of long-range correlated noise

TL;DR

This paper introduces a novel SVD-based method to reduce the impact of various trends on detrended fluctuation analysis, improving the reliability of detecting long-range correlations in noisy data.

Contribution

The paper presents a new SVD-based approach to mitigate trend effects in DFA, enhancing its robustness against linear, power-law, and periodic trends.

Findings

Effective trend removal demonstrated on real data sets

Improved accuracy in estimating scaling exponents

Method applicable to diverse trend types

Abstract

Detrended fluctuation analysis (DFA) has been proposed as a robust technique to determine possible long-range correlations in power-law processes [1]. However, recent studies have reported the susceptibility of DFA to trends [2] which give rise to spurious crossovers and prevent reliable estimation of the scaling exponents. Inspired by these reports, we propose a technique based on singular value-decomposition (SVD) of the trajectory matrix to minimize the effect of linear, power-law, periodic and also quasi-periodic trends superimposed on long-range correlated power-law noise. The effectiveness of the technique is demonstrated on publicly available data sets [2].