dc.contributor.author |
Ignaccolo, M |
|
dc.contributor.author |
Latka, M |
|
dc.contributor.author |
West, BJ |
|
dc.date.accessioned |
2011-06-21T17:30:32Z |
|
dc.date.available |
2011-06-21T17:30:32Z |
|
dc.date.issued |
2010 |
|
dc.identifier.citation |
Ignaccolo,M.;Latka,M.;West,B. J.. 2010. Detrended fluctuation analysis of scaling
crossover effects. Epl 90(1): 10009-10009.
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|
dc.identifier.issn |
0295-5075 |
|
dc.identifier.uri |
https://hdl.handle.net/10161/4406 |
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dc.description.abstract |
Detrended fluctuation analysis (DFA) is one of the most frequently used fractal time
series algorithms. DFA has also become the tool of choice for analysis of the short-time
fluctuations despite the fact that its validity in this domain has never been demonstrated.
We adopt an Ornstein-Uhlenbeck Langevin equation to generate a time series which exhibits
short-time power-law scaling and incorporates the fundamental property of physiological
control systems-negative feedback. To determine the scaling exponent, we derive the
analytical expressions for the standard deviation of the solution X(t) of this equation
using both the ensemble of statistically independent trajectories and the ensemble
obtained by partitioning a single trajectory. The latter approach is used in DFA and
many other physiological applications. Surprisingly, the formulas for the standard
deviations are different for these two ensembles. We demonstrate that the partitioning
amounts to building up deterministic trends that satisfy the "trend + signal" decomposition
assumption which is characteristic of DFA. Consequently, the dependence of the rms
of DFA residuals F(tau) on the length tau of data window is the same for both ensembles.
The growth of F(tau) is significantly different from that of the standard deviation
of X(t). While the DFA estimate of the short-time scaling exponent is correct, the
polynomial detrending delays the approach of F(tau) to the asymptotic value by as
much as an order of magnitude. This delay may underlie the gradual change of the DFA
scaling index typically observed in time series that exhibit crossover between the
short- and long-time scaling. Copyright (C) EPLA, 2010
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dc.language.iso |
en_US |
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dc.publisher |
IOP Publishing |
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dc.relation.isversionof |
10.1209/0295-5075/90/10009 |
|
dc.subject |
heart-rate dynamics |
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dc.subject |
time-series |
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dc.subject |
physics, multidisciplinary |
|
dc.title |
Detrended fluctuation analysis of scaling crossover effects |
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dc.title.alternative |
|
|
dc.type |
Other article |
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dc.description.version |
Version of Record |
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duke.date.pubdate |
2010-4-0 |
|
duke.description.issue |
1 |
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duke.description.volume |
90 |
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dc.relation.journal |
Epl |
|
pubs.begin-page |
10009 |
|
pubs.end-page |
10009 |
|