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<P><A NAME="SECTIONREF"><H2>References</H2></A><P>
<DL COMPACT>
<DT><A NAME="SFI"><STRONG>1</STRONG></A><DD>
A. S. Weigend and N. A. Gershenfeld, eds.,
``Time Series Prediction: Forecasting the future and understanding the
past'',
Santa Fe Institute Studies in the Science of Complexity, Proc. Vol. XV,
Addison-Wesley, Reading, MA (1993).
<P>
<DT><A NAME="coping"><STRONG>2</STRONG></A><DD>
E. Ott, T. Sauer, and J. A. Yorke,
``Coping with Chaos'',
Wiley, New York (1994).
<P>
<DT><A NAME="abarbook"><STRONG>3</STRONG></A><DD>
H. D. I. Abarbanel,
``Analysis of Observed Chaotic Data'',
Springer-Verlag, Berlin, Heidelberg, New York (1996).
<P>
<DT><A NAME="ourbook"><STRONG>4</STRONG></A><DD>
H. Kantz and T. Schreiber,
``Nonlinear Time Series Analysis''.
Cambridge University Press, Cambridge (1997).
<P>
<DT><A NAME="habil"><STRONG>5</STRONG></A><DD>
T. Schreiber,
<EM>Interdisciplinary application of nonlinear time series methods</EM>,
Phys. Reports <B>308</B>, 1 (1998).
<P>
<DT><A NAME="theiler1"><STRONG>6</STRONG></A><DD>
J. Theiler, S. Eubank, A. Longtin, B. Galdrikian, and J. D. Farmer,
<EM>Testing for nonlinearity in time series: The method of surrogate data</EM>,
Physica D <B>58</B>, 77 (1992); Reprinted in [<A HREF="node36.html#coping" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/surropaper/node36.html#coping">2</A>].
<P>
<DT><A NAME="theiler-sfi"><STRONG>7</STRONG></A><DD>
J. Theiler, P. S. Linsay, and D. M. Rubin,
<EM>Detecting nonlinearity in data with long coherence times</EM>,
in [<A HREF="node36.html#SFI" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/surropaper/node36.html#SFI">1</A>].
<P>
<DT><A NAME="fields"><STRONG>8</STRONG></A><DD>
J. Theiler and D. Prichard,
<EM>Using `Surrogate Surrogate Data' to calibrate the actual rate of
false positives in tests for nonlinearity in time series</EM>,
Fields Inst. Comm. <B>11</B>, 99 (1997).
<P>
<DT><A NAME="tisean"><STRONG>9</STRONG></A><DD>
R. Hegger, H. Kantz, and T. Schreiber,
<EM>Practical implementation of nonlinear time series methods: The
TISEAN package</EM>,
CHAOS <B>9</B>, 413 (1999).
The software package is publicly available at <TT>
http://www.mpipks-dresden.mpg.de/<IMG WIDTH=11 HEIGHT=4 ALIGN=BOTTOM ALT="tex2html_wrap_inline2584" SRC="img221.gif" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/surropaper/img221.gif">tisean</TT>.
<P>
<DT><A NAME="BI"><STRONG>10</STRONG></A><DD>
T. Subba Rao and M. M. Gabr,
``An introduction to bispectral analysis and bilinear time series models'',
Lecture notes in statistics Vol. 24,
Springer-Verlag, Berlin, Heidelberg, New York (1984).
<P>
<DT><A NAME="diks2"><STRONG>11</STRONG></A><DD>
C. Diks, J. C. van Houwelingen, F. Takens, and J. DeGoede,
<EM>Reversibility as a criterion for discriminating time series</EM>,
Phys. Lett. A <B>201</B>, 221 (1995).
<P>
<DT><A NAME="Timmer1"><STRONG>12</STRONG></A><DD>
J. Timmer, C. Gantert, G. Deuschl, and J. Honerkamp,
<EM>Characteristics of hand tremor time series</EM>,
Biol. Cybern. <B>70</B>, 75 (1993).
<P>
<DT><A NAME="power"><STRONG>13</STRONG></A><DD>
T. Schreiber and A. Schmitz,
<EM>Discrimination power of measures for nonlinearity in a time series</EM>,
Phys. Rev. E <B>55</B>, 5443 (1997).
<P>
<DT><A NAME="milan2"><STRONG>14</STRONG></A><DD>
M. Palus,
<EM>Testing for nonlinearity using redundancies: Quantitative and
qualitative aspects</EM>,
Physica D <B>80</B>, 186 (1995).
<P>
<DT><A NAME="pompe"><STRONG>15</STRONG></A><DD>
B. Pompe,
<EM>Measuring statistical dependencies in a time series</EM>,
J. Stat. Phys. <B>73</B>, 587 (1993).
<P>
<DT><A NAME="pt"><STRONG>16</STRONG></A><DD>
D. Prichard and J. Theiler,
<EM>Generalized redundancies for time series analysis</EM>,
Physica D <B>84</B>, 476 (1995).
<P>
<DT><A NAME="hao"><STRONG>17</STRONG></A><DD>
B.-L. Hao,
``Elementary Symbolic Dynamics'',
World Scientific, Singapore (1989).
<P>
<DT><A NAME="FNN"><STRONG>18</STRONG></A><DD>
M. B. Kennel, R. Brown, and H. D. I. Abarbanel,
<EM>Determining embedding dimension for phase-space reconstruction using
a geometrical construction</EM>,
Phys. Rev. A <B>45</B> 3403 (1992); Reprinted in [<A HREF="node36.html#coping" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/surropaper/node36.html#coping">2</A>].
<P>
<DT><A NAME="PM"><STRONG>19</STRONG></A><DD>
D. Pierson and F. Moss,
<EM>Detecting periodic unstable points in noisy chaotic and limit cycle
attractors with applications to biology</EM>,
Phys. Rev. Lett. <B>75</B>, 2124 (1995).
<P>
<DT><A NAME="soso"><STRONG>20</STRONG></A><DD>
P. So, E. Ott, S. J. Schiff, D. T. Kaplan, T. Sauer, and C. Grebogi,
<EM>Detecting unstable periodic orbits in chaotic experimental data</EM>,
Phys. Rev. Lett. <B>76</B>, 4705 (1996).
<P>
<DT><A NAME="volterra"><STRONG>21</STRONG></A><DD>
M. Barahona and C.-S. Poon,
<EM>Detection of nonlinear dynamics in short, noisy time series</EM>,
Nature <B>381</B>, 215 (1996).
<P>
<DT><A NAME="skinner"><STRONG>22</STRONG></A><DD>
J. E. Skinner, M. Molnar, and C. Tomberg,
<EM>The point correlation dimension: Performance with nonstationary
surrogate data and noise</EM>,
Integrative Physiological and Behavioral Science <B>29</B>, 217 (1994).
<P>
<DT><A NAME="roulston"><STRONG>23</STRONG></A><DD>
M. S. Roulston,
<EM>Significance testing on information theoretic functionals</EM>,
Physica D <B>110</B>, 62 (1997).
<P>
<DT><A NAME="witt"><STRONG>24</STRONG></A><DD>
K. Dolan, A. Witt, M. L. Spano, A. Neiman, and F. Moss,
<EM>Surrogates for finding unstable periodic orbits in noisy data sets</EM>,
Phys. Rev. E <B>59</B>, 5235 (1999).
<P>
<DT><A NAME="tp"><STRONG>25</STRONG></A><DD>
J. Theiler and D. Prichard,
<EM>Constrained-realization Monte-Carlo method for hypothesis testing</EM>,
Physica D <B>94</B>, 221 (1996).
<P>
<DT><A NAME="anneal"><STRONG>26</STRONG></A><DD>
T. Schreiber,
<EM>Constrained randomization of time series data</EM>,
Phys. Rev. Lett. <B>80</B>, 2105 (1998).
<P>
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