Open Access
Effect of Nonstationarities on Detrended Fluctuation Analysis
TLDR
It is found that introducing nonstationarities to stationary correlated signals leads to the appearance of crossovers in the scaling behavior and it is shown how to develop strategies for preprocessing "raw" data prior to analysis, which will minimize the effects of non stationarities on the scaling properties of the data.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.read more
Citations
More filters
Journal ArticleDOI
Multifractal Detrended Fluctuation Analysis of Nonstationary Time Series
Jan W. Kantelhardt,Jan W. Kantelhardt,Stephan Zschiegner,Eva Koscielny-Bunde,Eva Koscielny-Bunde,Shlomo Havlin,Shlomo Havlin,Armin Bunde,H. Eugene Stanley +8 more
TL;DR: In this article, the authors developed a method for the multifractal characterization of nonstationary time series, which is based on a generalization of the detrended fluctuation analysis (DFA).
Journal ArticleDOI
Gait dynamics in Parkinson’s disease: Common and distinct behavior among stride length, gait variability, and fractal-like scaling
TL;DR: This update highlights the idea that while stride length, gait variability, and fractal scaling of gait are all impaired in PD, distinct mechanisms likely contribute to and are responsible for the regulation of these disparate gait properties.
Journal ArticleDOI
Walking speed influences on gait cycle variability.
TL;DR: Findings are consistent with those previously shown in running studies and support the hypothesis that reduced strength of long range correlations at preferred locomotion speeds is reflective of enhanced stability and adaptability at these speeds.
Journal ArticleDOI
Comparison of detrended fluctuation analysis and spectral analysis for heart rate variability in sleep and sleep apnea
TL;DR: Investigation of the effect of sleep stages and sleep apnea on autonomic activity by analyzing heart rate variability concludes that changes in HRV are better quantified by scaling analysis than by spectral analysis.
Journal ArticleDOI
DCCA cross-correlation coefficient: Quantifying level of cross-correlation
TL;DR: In this paper, a new coefficient is proposed with the objective of quantifying the level of cross-correlation between nonstationary time series, which is defined in terms of the DFA method and the DCCA method.
References
More filters
Journal ArticleDOI
Mosaic organization of DNA nucleotides
Chung-Kang Peng,Chung-Kang Peng,Chung-Kang Peng,Sergey V. Buldyrev,Sergey V. Buldyrev,Sergey V. Buldyrev,Shlomo Havlin,Shlomo Havlin,Shlomo Havlin,Michael Simons,Michael Simons,Michael Simons,H. E. Stanley,H. E. Stanley,H. E. Stanley,Ary L. Goldberger,Ary L. Goldberger,Ary L. Goldberger +17 more
TL;DR: This work analyzes two classes of controls consisting of patchy nucleotide sequences generated by different algorithms--one without and one with long-range power-law correlations, finding that both types of sequences are quantitatively distinguishable by an alternative fluctuation analysis method.
Journal ArticleDOI
Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series
TL;DR: A new method--detrended fluctuation analysis (DFA)--for quantifying this correlation property in non-stationary physiological time series is described and application of this technique shows evidence for a crossover phenomenon associated with a change in short and long-range scaling exponents.
Journal ArticleDOI
Multifractality in human heartbeat dynamics
Plamen Ch. Ivanov,Plamen Ch. Ivanov,Luís A. Nunes Amaral,Luís A. Nunes Amaral,Ary L. Goldberger,Shlomo Havlin,Michael Rosenblum,Zbigniew R. Struzik,H. Eugene Stanley +8 more
TL;DR: In this paper, the authors investigate the possibility that time series generated by certain physiological control systems may be members of a special class of complex processes, termed multifractal, which require a large number of exponents to characterize their scaling properties.
Journal ArticleDOI
Long-range correlations in nucleotide sequences
Chung-Kang Peng,Sergey V. Buldyrev,Ary L. Goldberger,Shlomo Havlin,Shlomo Havlin,Francesco Sciortino,Michael Simons,Michael Simons,H. E. Stanley +8 more
TL;DR: This work proposes a method for studying the stochastic properties of nucleotide sequences by constructing a 1:1 map of the nucleotide sequence onto a walk, which it refers to as a 'DNA walk', and uncovers a remarkably long-range power law correlation.