<!--#set var="TITLE" value="Effect of Nonstationarities on Detrended Fluctuation Analysis"-->
<!--#set var="USELOCALCSS" value="1"-->
<!--#include virtual="/head.shtml"-->
<p style="text-align: center;">Zhi Chen<sup>1</sup>, Plamen Ch. Ivanov<sup>1, 2</sup>,
Kun Hu<sup>1</sup>, and H. Eugene Stanley<sup>1</sup> </p>
</p>
<p style="font-size: 90%;"> <sup>1</sup> Center for Polymer Studies and Department of Physics,
Boston University, Boston, Massachusetts 02215<br>
<sup>2</sup> Harvard Medical School, Beth Israel Deaconess Medical
Center, Boston, Massachusetts 02215<br>
</p>
<div class="notice">
<p>This article originally appeared in <em>Physical Review E</em>,
vol. 65, 041107, 2002 (©2002 <i>The American Physical Society</i>,<a
href="http://link.aps.org/abstract/PRE/v65/e041107" target="other">
http://link.aps.org/abstract/PRE/v65/e041107</a>). Please cite this
publication when referencing this material. </p>
</div>
<h2>Abstract</h2>
<p> Detrended fluctuation analysis (DFA) is a scaling analysis method
used to quantify long-range power-law correlations in signals. Many
physical and biological signals are "noisy," heterogeneous, and exhibit
different types of nonstationarities, which can affect the correlation
properties of these signals. We systematically study the effects of
three types of nonstationarities often encountered in real data.
Specifically, we consider nonstationary sequences formed in three ways:
(i) stitching together segments of data obtained from discontinuous
experimental recordings, or removing some noisy and unreliable parts
from continuous recordings and stitching together the remaining
parts--a "cutting" procedure commonly used in preparing data prior to
signal analysis; (ii) adding to a signal with known correlations a
tunable concentration of random outliers or spikes with different
amplitudes; and (iii) generating a signal comprised of segments with
different properties--e.g., different standard deviations or different
correlation exponents. We compare the difference between the scaling
results obtained for stationary correlated signals and correlated
signals with these three types of nonstationarities. We find that
introducing nonstationarities to stationary correlated signals leads to
the appearance of crossovers in the scaling behavior and we study how
the characteristics of these crossovers depend on (a) the fraction and
size of the parts cut out from the signal, (b) the concentration of
spikes and their amplitudes (c) the proportion between segments with
different standard deviations or different correlations and (d) the
correlation properties of the stationary signal. We show how to develop
strategies for preprocessing "raw" data prior to analysis, which will
minimize the effects of nonstationarities on the scaling properties of
the data, and how to interpret the results of DFA for complex signals
with different local characteristics.</p>
<ul>
<li>The original full paper is available (in PDF format) at: <a
href="http://link.aps.org/abstract/PRE/v65/e041107" target="other">
http://link.aps.org/abstract/PRE/v65/e041107</a> </li>
<li>An online HTML version is available <a
href="dfa2web.html"> here </a> which incorporates minor
revisions for publication on PhysioNet </li>
<li>The software described in this article is available <a
href="/physiotools/dfa/">here</a>. </li>
<li>The dataset is available <a href="../">here</a>. </li>
</ul>
<p style="font-size: 90%;">
<b> Address for correspondence: </b> <br>
Plamen Ch. Ivanov, Ph.D. <br>
Room 247, Dept. of Physics<br>
Boston Univeristy<br>
590 Commonwealth Avenue <br>
Boston, MA 02215, USA<br>
Email: <a href="mailto:plamen@buphy.bu.edu">plamen@buphy.bu.edu</a></p>
<!--#include virtual="/dir-footer.shtml"-->