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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Effects of non-stationarity on the magnitude and sign scaling in the multi-scale vertical velocity increment
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Entropy Analysis of RR-Time Series From Stress Tests.
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Decoding the Morphological Differences between Himalayan Glacial and Fluvial Landscapes Using Multifractal Analysis
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Discriminating brain activity from task-related artifacts in functional MRI: fractal scaling analysis simulation and application.
Jae-Min Lee,Jing Hu,Jianbo Gao,Bruce Crosson,Kyung K. Peck,Christina E. Wierenga,Keith M. McGregor,Qun Zhao,Keith D. White +8 more
TL;DR: Simulations further corroborate that DFA is excellent at discriminating signal changes due totask-related brain activities from those due to task-related artifacts, under a range of conditions.
References
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