Quantifying signals with power-law correlations: A comparative study of detrended fluctuation analysis and detrended moving average techniques

TL;DR

This study compares the effectiveness of DFA and DMA methods in quantifying power-law correlations in non-stationary signals, highlighting how their performance depends on method variants and signal properties.

Contribution

It systematically evaluates different DMA variants against DFA, revealing their dependence on filter types and establishing optimal regimes for accurate scaling exponent estimation.

Findings

DMA results vary with filter type

Optimal scaling regimes depend on signal correlations

A 3D representation shows stability factors for DFA and DMA

Abstract

Detrended fluctuation analysis (DFA) and detrended moving average (DMA) are two scaling analysis methods designed to quantify correlations in noisy non-stationary signals. We systematically study the performance of different variants of the DMA method when applied to artificially generated long-range power-law correlated signals with an {\it a-priori} known scaling exponent $\alpha_{0}$ and compare them with the DFA method. We find that the scaling results obtained from different variants of the DMA method strongly depend on the type of the moving average filter. Further, we investigate the optimal scaling regime where the DFA and DMA methods accurately quantify the scaling exponent $\alpha_{0}$, and how this regime depends on the correlations in the signal. Finally, we develop a three-dimensional representation to determine how the stability of the scaling curves obtained from the DFA and DMA methods depends on the scale of analysis, the order of detrending, and the order of the moving average we use, as well as on the type of correlations in the signal.