Effect of nonstationarities on detrended fluctuation analysis.

By Z. Chen, Plamen Ch. Ivanov, K. Hu, H. University, H. School. Physical review. E, Statistical, nonlinear, and soft matter physics, 2001

875 citations recorded by the source corpus.

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.

Subfields: Computer Networks and Communications, Economics and Econometrics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/f813c1d04a77e9c7bbf5d5b2bc52f1b20e9b6f8d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Networks and Communications

In Economics and Econometrics

In Molecular Biology

Citations in the corpus

Tempting long-memory - on the interpretation of DFA results (2004, background): “The ability of DFA to estimateα from realizations of long-memory processes corrupted by different instationarities like trends, spikes, harmonics and gaps has been studied byHu et al.(2001), Chen et al.(2002) and Kantelhardt et al.(2001).”
Detrended Fluctuation Analysis: A Scale-Free View on Neuronal Oscillations (2012, methodology): “Since DFA was first introduced several papers have tested the performance of DFA in relation to trends (Hu et al., 2001), nonstationarities (Chen et al., 2002), pre-processing such as artifact rejection (Chen et al., 2002), and coarse-graining (Xu et al., 2011).”
Autocorrelation and cross-correlation in time series of homicide and attempted homicide (2014, neutral): “[24, 29,33,39–47], among others.”
Time-dependent Hurst exponent in financial time series (2004, methodology): “According to the DFA method [10–12], after dividing the series yðtÞ in boxes of equal size n, a polynomial fit ypolðtÞ is calculated in each box.”
Long‐range persistence in global Aerosol Index dynamics (2006, background): “…proved to satisfy this criterion is the wellestablished DFA, which stems from random walk theory and permits the detection of intrinsic self-similarity in non-stationary time series (Peng et al. 1994, Perez and Trier 2001, Weber and Talkner 2001, Chen et al. 2002, Varotsos et al. 2003a,b, 2005).”
Multi-scaling in finance (2007, background): “…et al. 1997, Ausloos et al. 1999, Janosi et al. 1999, Liu et al. 1999, Raberto et al. 1999, Stanley et al. 1999, Ausloos 2000, Hu et al. 2001, Chen et al. 2002, Ivanova and Ausloos 2002, Costa and Vasconcelos 2003) and its generalization (Kantelhardt et al. 2002, Matia et al. 2003,…”