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
More filters
Journal ArticleDOI
Characterizing variability and predictability for air pollutants with stochastic models.
TL;DR: In this paper, the authors investigate the dynamics of particulate matter, nitrogen oxides, and ozone concentrations in Hong Kong using fluctuation functions as a measure for their variability, and develop several simple data models and test their predictive power.
Journal ArticleDOI
Long-term stability of resting state EEG-based linear and nonlinear measures.
TL;DR: The results support the prospect of using EEG-based measures in clinical practice by indicating that the stability is highest for the nonlinear (HFD and DFA) and the linear (relative powers of EEG frequency bands) EEG measures that use the signal from a single EEG channel and frequency band.
Journal ArticleDOI
On the Autocorrelation Function of 1/f Noises
Pedro Carpena,Ana V. Coronado +1 more
TL;DR: In this article , an analytical derivation of C(k) for 1/fβ noises has been provided, and they show the validity of their results by comparing them with the numerical results obtained from synthetically generated 1 /fβ time series.
DissertationDOI
Gait variability, stride dynamics and falls risk in community dwelling older women
TL;DR: In this paper, the authors investigated the effect of walking protocol on measures of gait variability in healthy adults and examined the relationship between stride dynamics, gait variance and falls in older adults.
Journal ArticleDOI
Robustness of Estimators of Long-Range Dependence and Self-Similarity under non-Gaussianity
Christian Franzke,Timothy Graves,Nicholas W. Watkins,Robert B. Gramacy,Robert B. Gramacy,Cecilia Hughes +5 more
TL;DR: In this article, two paradigmatic models are discussed which can simultaneously account for long-range dependence and non-Gaussianity: autoregressive fractional integrated moving average (ARFIMA) and linear fractional stable motion (LFSM).
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
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
Detecting long-range correlations with detrended fluctuation analysis
TL;DR: It is shown that deviations from scaling which appear at small time scales become stronger in higher orders of detrended fluctuation analysis, and a modified DFA method is suggested to remove them.
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.