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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Duration specificity in the long-range correlation of human serial interval production
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Multifractals embedded in short time series: An unbiased estimation of probability moment.
TL;DR: The factorial-moment-based estimation can evaluate correctly the scaling behaviors in a scale range about three generations wider than the multifractal detrended fluctuation analysis and the basic estimation, and can provide an unbiased estimation of the probability moments of continuous order.
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Fractal behavior of traffic volume on urban expressway through adaptive fractal analysis
TL;DR: Wang et al. as mentioned in this paper investigated the fractal behavior of traffic volume in urban expressway based on a newly developed adaptive fractal analysis (AFA), which has a number of advantages over traditional method of detrended fluctuation analysis (DFA).
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Alteration in scaling behavior of short-term heartbeat time series for professional shooting athletes from rest to exercise
TL;DR: It is demonstrated that during exercise stronger correlations appear in the heartbeat series of shooting athletes in order to satisfy the specific requirements for high concentration and better control on their heart beats.
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Time series analysis of monthly rainfall in Nigeria with emphasis on self-organized criticality
TL;DR: In this paper, the rescaled range (R/S) statistic, the standard fluctuation analysis (FA) and the detrended fluctuation analyses (DFA) were used to analyze monthly rainfall data of twenty-one years (1980-2000).
References
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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.
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Detecting long-range correlations with detrended fluctuation analysis
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Journal ArticleDOI
Estimators for long-range dependence: an empirical study
TL;DR: In this paper, various methods for estimating the self-similarity parameter and/or the intensity of long-range dependence in a time series are available. But some of these methods are more reliable than others.