Detrended fluctuation analysis of power-law-correlated sequences with random noises

TL;DR

This paper investigates how short-range random noises impact the analysis of long-range correlations in temporal data, demonstrating DFA's robustness and providing practical methods to recover true correlations.

Contribution

It introduces an analysis of noise effects on DFA and proposes coarse-graining techniques to recover long-range correlations in noisy sequences.

Findings

DFA can extract long-range correlations despite short-range noise.

Short-range noise hampers power-spectrum analysis of correlations.

Coarse-grained sequences help recover true long-range correlations.

Abstract

Improvement in time resolution sometimes introduces short-range random noises into temporal data sequences. These noises affect the results of power-spectrum analyses and the Detrended Fluctuation Analysis (DFA). The DFA is one of useful methods for analyzing long-range correlations in non-stationary sequences. The effects of noises are discussed based on artificial temporal sequences. Short-range noises prevent power-spectrum analyses from detecting long-range correlations. The DFA can extract long-range correlations from noisy time sequences. The DFA also gives the threshold time length, under which the noises dominate. For practical analyses, coarse-grained time sequences are shown to recover long-range correlations.