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
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References
More filters
Journal ArticleDOI
Long-Term Storage Capacity of Reservoirs
TL;DR: In this paper, a solution of the problem of determining the reservoir storage required on a given stream, to guarantee a given draft, is presented, where a long-time record of annual total...
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
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Journal ArticleDOI
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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.