<!--#set var="TITLE" value="Surrogate Data with Correlations, Trends, and Nonstationarities"-->
<!--#set var="USELOCALCSS" value="1"-->
<!--#include virtual="/head.shtml"-->
<div class="notice">
<p>
These data were contributed by Plamen Ch. Ivanov, Zhi Chen and Kun Hu, who
used them in:</p>
<div class="reference">
Hu K, Ivanov PCh, Chen Z, Carpena P, Stanley HE.
<a href="paper1/">Effects of trends on detrended fluctuation analysis</a>.
<i>Phys Rev E</i> 2001; <b>64</b>:011114.
</div> <!-- end reference -->
<div class="reference">
Chen Z, Ivanov PCh, Hu K, Stanley HE.
<a href="paper2/">Effects of nonstationarities on detrended fluctuation
analysis</a>. <i>Phys Rev E</i> 2002; <b>65</b>:041107.
</div> <!-- end reference -->
<p><b>Please cite these publications when referencing this material, and
also include the standard citation for PhysioNet:</b></p>
<div class="reference">
Goldberger AL, Amaral LAN, Glass L, Hausdorff JM, Ivanov PCh, Mark RG,
Mietus JE, Moody GB, Peng C-K, Stanley HE. PhysioBank, PhysioToolkit, and
PhysioNet: Components of a New Research Resource for Complex Physiologic
Signals.
<i>Circulation</i> <b>101</b>(23):e215-e220 [Circulation Electronic Pages;
<a href="http://circ.ahajournals.org/content/101/23/e215.full"
target="other">http://circ.ahajournals.org/content/101/23/e215.full</a>];
2000 (June 13).
</a>
</div> <!-- end reference -->
</div>
<p>
The data in this collection include: (1) 6 surrogate stationary signals with
different correlations; (2) 7 surrogate correlated signals with linear,
sinusoidal and power-law trends; and (3) 15 surrogate correlated signals with
different types of nonstationarities. Each data file contains one column of
data in ASCII format. Results on correlated signals with trends are discussed
in <a href="paper1/">Physical Review E 64, 011114 (2001)</a>. Results on
correlated signals with different types of nonstationarities are discussed in
<a href="paper2/">Physical Review E 65, 041107 (2002)</a>. The parameter
"alpha" (see below) is an exponent measuring the degree of correlations in a
signal, and Nmax is the signal length. A detailed description of these signals
can be found in the original articles.</p>
<p>
Correlations in these signals
can be quantified using <a href="/physiotools/dfa/">Detrended Fluctuation
Analysis (DFA)</a>.
Limitations of the DFA method are discussed in the articles cited above.
In particular, the second paper notes that</p>
<blockquote>
... for anti-correlated signals, the scaling exponent obtained from the DFA
method overestimates the true correlations at small scales. To avoid this
problem, one needs first to integrate the original anti-correlated signal and
then apply the DFA method. The correct scaling exponent can thus be obtained
from the relation between <i>n</i> [the DFA box length] and <i>F(n)/n</i>
instead of <i>F(n)</i> ... In order to provide a more accurate estimate of
<i>F(n)</i>, the largest box size <i>n</i> we use is <i>N<font
size=-1><sub>max</sub></font>/10</i>, where <i>N<font
size=-1><sub>max</sub></font></i> is the total number of points in the signal.
</blockquote>
<p>
Since these files are quite large, they are provided as gzip-compressed text.</p>
<h4>1. Correlated stationary signals</h4>
<ul>
<li><a href="noise0117.txt.gz"> noise0117.txt.gz</a> alpha = 0.1,
<i>N<font size=-1><sub>max</sub></font></i> = 2<sup><small>17</small></sup>; </li>
<li><a href="noise0217.txt.gz"> noise0217.txt.gz</a> alpha = 0.2,
<i>N<font size=-1><sub>max</sub></font></i> = 2<sup><small>17</small></sup>; </li>
<li><a href="noise0517.txt.gz"> noise0517.txt.gz</a> alpha = 0.5,
<i>N<font size=-1><sub>max</sub></font></i> = 2<sup><small>17</small></sup>; </li>
<li><a href="noise0817.txt.gz"> noise0817.txt.gz</a> alpha = 0.8,
<i>N<font size=-1><sub>max</sub></font></i> = 2<sup><small>17</small></sup>; </li>
<li><a href="noise0917.txt.gz"> noise0917.txt.gz</a> alpha = 0.9,
<i>N<font size=-1><sub>max</sub></font></i> = 2<sup><small>17</small></sup>; </li>
<li><a href="noise1517.txt.gz"> noise1517.txt.gz</a> alpha = 1.5,
<i>N<font size=-1><sub>max</sub></font></i> = 2<sup><small>17</small></sup>. </li>
</ul>
<h4>2. Surrogate signals with trends </h4>
<p> 2a) Signals with linear trends </p>
<ul>
<li><a href="trlina1.txt.gz"> trlina1.txt.gz</a> alpha = 0.1,
<i>N<font size=-1><sub>max</sub></font></i> = 2<sup><small>17</small></sup>, slope of linear trend A<font=-1><sub>l</sub></font> = 2<sup><small>-16</small></sup> / index; </li>
<li><a href="trlina2.txt.gz"> trlina2.txt.gz</a> alpha = 0.1,
<i>N<font size=-1><sub>max</sub></font></i> = 2<sup><small>17</small></sup>, slope of linear trend A<font=-1><sub>l</sub></font> = 2<sup><small>-12</small></sup> / index; </li>
<li><a href="trlina3.txt.gz"> trlina3.txt.gz</a> alpha = 0.1,
<i>N<font size=-1><sub>max</sub></font></i> = 2<sup><small>17</small></sup>, slope of linear trend A<font=-1><sub>l</sub></font> = 2<sup><small>-8</small></sup> / index. </li>
</ul>
2b) Signals with sinusoidal trends <br>
<ul>
<li><a href="trsin1.txt.gz"> trsin1.txt.gz</a> alpha = 0.9,
<i>N<font size=-1><sub>max</sub></font></i> = 2<sup><small>17</small></sup>, Amplitude of trend A<font=-1><sub>s</sub></font> = 2, period T = 128; </li>
<li><a href="trsin2.txt.gz"> trsin2.txt.gz</a> alpha = 0.1,
<i>N<font size=-1><sub>max</sub></font></i> = 2<sup><small>17</small></sup>, Amplitude of trend A<font=-1><sub>s</sub></font> = 2, period T = 128. </li>
</ul>
2c) Signals with power-law trends <br>
<ul>
<li><a href="trpow1.txt.gz"> trpow1.txt.gz</a> alpha = 0.9,
<i>N<font size=-1><sub>max</sub></font></i> = 2<sup><small>17</small></sup>, power lambda = 0.4, Amplitude A<font=-1><sub>p</sub></font> = 1000 / (<i>N<font size=-1><sub>max</sub></font></i>) <sup><small>lambda</small></sup>; </li>
<li><a href="trpow2.txt.gz"> trpow2.txt.gz</a> alpha = 1.5,
<i>N<font size=-1><sub>max</sub></font></i> = 2<sup><small>17</small></sup>, power lambda = -0.7, Amplitude A<font=-1><sub>p</sub></font> = 0.01 / (<i>N<font size=-1><sub>max</sub></font></i>) <sup><small>lambda</small></sup>. </li>
</ul>
<h4>3. Surrogate nonstationary signals </h4>
<p> 3a) Signals with cutout segments (discontinuities) </p>
<ul>
<li><a href="cut0117w20p95.txt.gz"> cut0117w20p95.txt.gz</a>
alpha = 0.1, seg. cutout probability p = 0.05, Width W = 20, <i>N<font size=-1><sub>max</sub></font></i> = 2<sup><small>17</small></sup>; </li>
<li><a href="cut0117w20p50.txt.gz"> cut0117w20p50.txt.gz</a>
alpha = 0.1, seg. cutout probability p = 0.50, Width W = 20, <i>N<font size=-1><sub>max</sub></font></i> = 2<sup><small>17</small></sup>; </li>
<li><a href="cut0917w20p95.txt.gz"> cut0917w20p95.txt.gz</a>
alpha = 0.9, seg. cutout probability p = 0.05, Width W = 20, <i>N<font size=-1><sub>max</sub></font></i> = 2<sup><small>17</small></sup>; </li>
<li><a href="cut0917w20p50.txt.gz"> cut0917w20p50.txt.gz</a>
alpha = 0.9, seg. cutout probability p = 0.50, Width W = 20, <i>N<font size=-1><sub>max</sub></font></i> = 2<sup><small>17</small></sup>. </li>
</ul>
3b) Signals with spikes
<ul>
<li><a href="sp02p05a1.txt.gz"> sp02p05a1.txt.gz</a>
spikes probability p = 0.05, Amplitude Asp = 1,
<i>N<font size=-1><sub>max</sub></font></i> = 2<sup><small>17</small></sup>; </li>
<li><a href="sp02p05a1sp.txt.gz"> sp02p05a1sp.txt.gz</a>
spikes signal only, spikes probability p = 0.05, Amplitude Asp = 1,
<i>N<font size=-1><sub>max</sub></font></i> = 2<sup><small>17</small></sup>; </li>
<li><a href="sp08p05a10.txt.gz"> sp08p05a10.txt.gz</a>
spikes probability p = 0.05, Amplitude Asp = 10, <i>N<font size=-1><sub>max</sub></font></i> = 2<sup><small>17</small></sup>; </li>
<li><a href="sp08p05a10sp.txt.gz"> sp08p05a10sp.txt.gz</a>
spikes signal only, spikes probability p = 0.05, Amplitude Asp = 10,
<i>N<font size=-1><sub>max</sub></font></i> = 2<sup><small>17</small></sup>. </li>
</ul>
3c) Signals with different local standard deviation
<ul>
<li><a href="d2h4pd050118s.txt.gz"> d2h4pd050118s.txt.gz</a>
alpha = 0.1, sigma<font size=-1><sub>1</sub></font> = 1, sigma<font size=-1><sub>2</sub></font> = 4 (probability p = 0.05), <i>N<font size=-1><sub>max</sub></font></i> = 2<sup><small>18</small></sup>; </li>
<li><a href="d2h4pd950118s.txt.gz"> d2h4pd950118s.txt.gz</a>
alpha = 0.1, sigma<font size=-1><sub>1</sub></font> = 1, sigma<font size=-1><sub>2</sub></font> = 4 (probability p = 0.95), <i>N<font size=-1><sub>max</sub></font></i> = 2<sup><small>18</small></sup>; </li>
<li><a href="d2h4pd050918s.txt.gz"> d2h4pd050918s.txt.gz</a>
alpha = 0.9, sigma<font size=-1><sub>1</sub></font> = 1, sigma<font size=-1><sub>2</sub></font> = 4 (probability p = 0.05), <i>N<font size=-1><sub>max</sub></font></i> = 2<sup><small>18</small></sup>; </li>
<li><a href="d2h4pd950918s.txt.gz"> d2h4pd950918s.txt.gz</a>
alpha = 0.9, sigma<font size=-1><sub>1</sub></font> = 1, sigma<font size=-1><sub>2</sub></font> = 4 (probability p = 0.95), <i>N<font size=-1><sub>max</sub></font></i> = 2<sup><small>18</small></sup>. </li>
</ul>
3d) Signals with different local correlations
<ul>
<li><a href="cut010917p90w20_sum.txt.gz"> cut010917p90w20_sum.txt.gz</a>
(mixed signal) alpha<font size=-1><sub>1</sub></font> = 0.1 (90%),
alpha<font size=-1><sub>2</sub></font> = 0.9(10%), Width = 20, <i>N<font size=-1><sub>max</sub></font></i> = 2<sup><small>17</small></sup>; </li>
<li><a href="cut010917p90w20_comp1.txt.gz"> cut010917p90w20_comp1.txt.gz</a>
(component 1) alpha<font size=-1><sub>1</sub></font> = 0.1 (90%) only, Width W = 20,
<i>N<font size=-1><sub>max</sub></font></i> = 2<sup><small>17</small></sup>; </li>
<li><a href="cut010917p90w20_comp2.txt.gz"> cut010917p90w20_comp2.txt.gz</a>
(component 2) alpha<font size=-1><sub>2</sub></font> = 0.9 (10%) only, Width W = 20,
<i>N<font size=-1><sub>max</sub></font></i> = 2<sup><small>17</small></sup>. </li>
</ul>
<p style="font-size: 90%;"> <br>
<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@meta.bu.edu">plamen@meta.bu.edu</a></p>
<!--#include virtual="/dir-footer.shtml"-->