Effect of nonstationarities on detrended fluctuation analysis

Zhi Chen, Plamen Ch. Ivanov, Kun Hu, and H. Eugene Stanley
Phys. Rev. E 65, 041107 – Published 8 April 2002
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Abstract

Detrended fluctuation analysis (DFA) is a scaling analysis method used to quantify long-range power-law correlations in signals. Many physical and biological signals are “noisy,” heterogeneous, and exhibit different types of nonstationarities, which can affect the correlation properties of these signals. We systematically study the effects of three types of nonstationarities often encountered in real data. Specifically, we consider nonstationary sequences formed in three ways: (i) stitching together segments of data obtained from discontinuous experimental recordings, or removing some noisy and unreliable parts from continuous recordings and stitching together the remaining parts—a “cutting” procedure commonly used in preparing data prior to signal analysis; (ii) adding to a signal with known correlations a tunable concentration of random outliers or spikes with different amplitudes; and (iii) generating a signal comprised of segments with different properties—e.g., different standard deviations or different correlation exponents. We compare the difference between the scaling results obtained for stationary correlated signals and correlated signals with these three types of nonstationarities. We find that introducing nonstationarities to stationary correlated signals leads to the appearance of crossovers in the scaling behavior and we study how the characteristics of these crossovers depend on (a) the fraction and size of the parts cut out from the signal, (b) the concentration of spikes and their amplitudes (c) the proportion between segments with different standard deviations or different correlations and (d) the correlation properties of the stationary signal. We show how to develop strategies for preprocessing “raw” data prior to analysis, which will minimize the effects of nonstationarities on the scaling properties of the data, and how to interpret the results of DFA for complex signals with different local characteristics.

  • Received 12 November 2001

DOI:https://doi.org/10.1103/PhysRevE.65.041107

©2002 American Physical Society

Authors & Affiliations

Zhi Chen1, Plamen Ch. Ivanov1,2, Kun Hu1, and H. Eugene Stanley1

  • 1Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215
  • 2Harvard Medical School, Beth Israel Deaconess Medical Center, Boston, Massachusetts 02215

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Vol. 65, Iss. 4 — April 2002

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