Effect of Nonstationarities on Detrended Fluctuation Analysis

Zhi Chen¹, Plamen Ch. Ivanov^{1, 2}, Kun Hu¹, and H. Eugene Stanley¹

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

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.

• The original full paper is available (in PDF format) at:   http://link.aps.org/abstract/PRE/v65/e041107
• An online HTML version is available here which incorporates minor revisions for publication on PhysioNet
• The software described in this article is available here.
• The dataset is available here.

Address for correspondence:
Plamen Ch. Ivanov, Ph.D.
Room 247, Dept. of Physics
Boston Univeristy
590 Commonwealth Avenue
Boston, MA 02215, USA
Email: plamen@buphy.bu.edu