Effect of trends on detrended fluctuation analysis.
TLDR
It is shown how to use DFA appropriately to minimize the effects of trends, how to recognize if a crossover indicates indeed a transition from one type to a different type of underlying correlation, or if the crossover is due to a trend without any transition in the dynamical properties of the noise.Abstract:
scaling behavior. We find that crossovers result from the competition between the scaling of the noise and the ‘‘apparent’’ scaling of the trend. We study how the characteristics of these crossovers depend on ~i! the slope of the linear trend; ~ii! the amplitude and period of the periodic trend; ~iii! the amplitude and power of the power-law trend, and ~iv! the length as well as the correlation properties of the noise. Surprisingly, we find that the crossovers in the scaling of noisy signals with trends also follow scaling laws—i.e., long-range power-law dependence of the position of the crossover on the parameters of the trends. We show that the DFA result of noise with a trend can be exactly determined by the superposition of the separate results of the DFA on the noise and on the trend, assuming that the noise and the trend are not correlated. If this superposition rule is not followed, this is an indication that the noise and the superposed trend are not independent, so that removing the trend could lead to changes in the correlation properties of the noise. In addition, we show how to use DFA appropriately to minimize the effects of trends, how to recognize if a crossover indicates indeed a transition from one type to a different type of underlying correlation, or if the crossover is due to a trend without any transition in the dynamical properties of the noise.read more
Citations
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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
Fractal dynamics in physiology: Alterations with disease and aging
Ary L. Goldberger,Luís A. Nunes Amaral,Jeffrey M. Hausdorff,Plamen Ch. Ivanov,C.-K. Peng,H. Eugene Stanley +5 more
TL;DR: Application of fractal analysis may provide new approaches to assessing cardiac risk and forecasting sudden cardiac death, as well as to monitoring the aging process, and similar approaches show promise in assessing other regulatory systems, such as human gait control in health and disease.
Journal ArticleDOI
Effect of nonstationarities on detrended fluctuation analysis.
TL;DR: In this article, the effects of three types of non-stationarities often encountered in real data were studied. And the authors compared the difference between the scaling results obtained for stationary correlated signals and correlated signals with these three types and showed how the characteristics of these crossovers depend on the fraction and size of the parts cut out from the signal, the concentration of spikes and their amplitudes.
Effect of Nonstationarities on Detrended Fluctuation Analysis
TL;DR: 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.
Journal ArticleDOI
Exploiting Nonlinear Recurrence and Fractal Scaling Properties for Voice Disorder Detection
TL;DR: Two new tools to speech analysis are introduced: recurrence and fractal scaling, which overcome the range limitations of existing tools by addressing directly these two symptoms of disorder, together reproducing a "hoarseness" diagram.
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