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<head><title>Nonlinear Time Series Routines</title></head>
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<h1>TISEAN 2.0: Table of Contents</h1>
<h3><a name="generating">
Generating time series</a></h3>
A few routines are provided to generate test data from simple
equations. Since there are powerfull packages (for example <a
href="../../../../tppmsgs/msgs0.htm#13" tppabs="http://keck2.umd.edu/dynamics/">Dynamics</a> by Helena Nusse and Jim
Yorke) that can generate chaotic data,
we have only included a minimal selection here.
<p><table border>
<tr><td>Make Hénon time series</td>
<td><a href="wuppertal/henon.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/wuppertal/henon.html">henon</a></td></tr>
<tr><td>Make Ikeda time series</td>
<td><a href="wuppertal/ikeda.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/wuppertal/ikeda.html">ikeda</a></td></tr>
<tr><td>Run autoregressive model</td>
<td><a href="wuppertal/ar-run.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/wuppertal/ar-run.html">ar-run</a></td></tr>
<tr><td>Add noise to data</td>
<td><a href="dresden/makenoise.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/dresden/makenoise.html">makenoise</a>,
<a href="wuppertal/addnoise.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/wuppertal/addnoise.html">addnoise</a></td></tr>
</table>
<h3><a name="linear">
Linear tools</a></h3>
This section contains some rather basic implementations of linear time series
methods which are there just for convenience. If you want to embark seriously
on linear or spectral analysis of your data, you will have to use any one of
the statistical or mathematics packages around. Please, don't judge us by the
level of sophistication in this section!
<p><table border>
<tr><td>AR model</td>
<td><a href="dresden/ar-model.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/dresden/ar-model.html">ar-model</a></td></tr>
<tr><td>Autocorrelation function</td>
<td><a href="dresden/corr.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/dresden/corr.html">corr</a>,
<a href="wuppertal/autocor.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/wuppertal/autocor.html">autocor</a></td></tr>
<tr><td>Autocorrelation function of event times</td>
<td><a href="wuppertal/spikeauto.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/wuppertal/spikeauto.html">spikeauto</a></td></tr>
<tr><td>Power spectrum</td>
<td><a href="dresden/mem_spec.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/dresden/mem_spec.html">mem_spec</a>,
<a href="wuppertal/spectrum.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/wuppertal/spectrum.html">spectrum</a></td></tr>
<tr><td>Power spectrum of event times</td>
<td><a href="wuppertal/spikespec.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/wuppertal/spikespec.html">spikespec</a></td></tr>
<tr><td>Notch filter</td>
<td><a href="wuppertal/notch.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/wuppertal/notch.html">notch</a></td></tr>
<tr><td>Wiener filter</td>
<td><a href="wuppertal/wiener.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/wuppertal/wiener.html">wiener</a></td></tr>
<tr><td>Simple low pass filter</td>
<td><a href="dresden/low121.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/dresden/low121.html">low121</a></tr>
</table>
<h3><a name="utilities">
Utilities</a></h3>
Here are some tools for the pre-processing of data which save you the truble of
writing your own five-line Perl, awk, FORTRAN or C programs.
<p><table border>
<tr><td>Choose sub-sequence or columns</td>
<td><a href="wuppertal/choose.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/wuppertal/choose.html">choose</a></td></tr>
<tr><td>Normalise, rescale, mean, standard deviation</td>
<td><a href="dresden/rescale.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/dresden/rescale.html">rescale</a>,
<a href="wuppertal/rms.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/wuppertal/rms.html">rms</a></td></tr>
<tr><td>Distribution of the data</td>
<td><a href="dresden/histogram.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/dresden/histogram.html">histogram</a></td></tr>
<tr><td>Change sampling time</td>
<td><a href="dresden/resample.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/dresden/resample.html">resample</a></tr>
<tr><td>Event/intervcal conversion</td>
<td><a href="wuppertal/intervals.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/wuppertal/intervals.html">intervals</a></td></tr>
<tr><td>Interval/event conversion</td>
<td><a href="wuppertal/events.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/wuppertal/events.html">events</a></td></tr>
</table>
<h3><a name="visual">
Stationarity</a></h3>
This section contains two important tools for the visualization of time series
properties and another stationarity test as proposed by <a
href="chaospaper/citation.html#statio" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/chaospaper/citation.html#statio">Schreiber</a>. The recurrence plot
and the space time separation plot are of great value for the detection of
nonstationarity, selection of relevant time scales, selection of stationary
episodes and so forth.
<p>
There is a short corresponding section in the
<a href="chaospaper/node13.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/chaospaper/node13.html">introduction</a> paper.
<p><table border>
<tr><td>Recurrence plot</td>
<td><a href="dresden/recurr.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/dresden/recurr.html">recurr</a></td></tr>
<tr><td>Space-time separation plot</td>
<td><a href="wuppertal/stp.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/wuppertal/stp.html">stp</a></td></tr>
<tr><td>Stationarity test</td>
<td><a href="dresden/nstat_z.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/dresden/nstat_z.html">nstat_z</a></td></tr>
</table>
<h3><a name="embedding">
Embedding and Poincaré sections</a></h3>
Since the concept of phase space is at the heart of all the nonlinear
methods in this package, phase space reconstruction plays an important role.
Although delay and other embeddings are used inside most of the other programs,
it is important to have these techniques also for data viewing, selection of
parameters, etc. For delay embeddings, use
<a href="wuppertal/delay.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/wuppertal/delay.html">delay</a>. For principal components,
<a href="dresden/svd.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/dresden/svd.html">svd</a> and
<a href="wuppertal/pc.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/wuppertal/pc.html">pc</a> do almost the same thing.
<p>
Phase space reconstruction is discussed also in the
the <a href="chaospaper/node5.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/chaospaper/node5.html">introduction</a> paper.
<p><table border>
<tr><td>Embed using delay coordinates</td>
<td><a href="wuppertal/delay.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/wuppertal/delay.html">delay</a></td></tr>
<tr><td>Embed using principal components</td>
<td><a href="dresden/svd.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/dresden/svd.html">svd</a>,
<a href="wuppertal/pc.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/wuppertal/pc.html">pc</a></td></tr>
<tr><td>Mutual information of the data</td>
<td><a href="dresden/mutual.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/dresden/mutual.html">mutual</a></tr>
<tr><td>Poincaré section</td>
<td><a href="dresden/poincare.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/dresden/poincare.html">poincare</a></tr>
<tr><td>Determine the extrema of a time series</td>
<td><a href="dresden/extrema.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/dresden/extrema.html">extrema</a></tr>
<tr><td>Unstable periodic orbits</td>
<td>
<a href="wuppertal/upo.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/wuppertal/upo.html">upo</a>,
<a href="wuppertal/upoembed.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/wuppertal/upoembed.html">upoembed</a></td></tr>
<tr><td>False nearest neighbours</td>
<td><a href="dresden/false_nearest.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/dresden/false_nearest.html">
false_nearest</a></tr>
</table>
<h3><a name="prediction">
Nonlinear prediction</a></h3>
A number of phase space based prediction techniques are implemented in TISEAN.
They differ in the way in which the dynamics is approximated. The very similar
programs <a href="dresden/zeroth.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/dresden/zeroth.html">zeroth</a> and
<a href="wuppertal/predict.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/wuppertal/predict.html">predict</a> use locally constant fits.
This is the most robust approach for short, noisy signals, easy handling and
quick answers. Further, local linear models, radial basis functions, and
polynomial fits are provided.
<p>
For a discussion of these methods and examples see the corresponding section of
the <a href="chaospaper/node16.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/chaospaper/node16.html">introduction</a> paper.
<p><table border>
<tr><td>Simple nonlinear prediction</td>
<td><a href="dresden/zeroth.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/dresden/zeroth.html">zeroth</a>,
<a href="wuppertal/predict.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/wuppertal/predict.html">predict</a></td></tr>
<tr><td>Local linear model</td>
<td><a href="dresden/onestep.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/dresden/onestep.html">onestep</a>,
<a href="dresden/nstep.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/dresden/nstep.html">nstep</a></tr>
<tr><td>Local vs. global linear prediction</td>
<td><a href="dresden/ll-ar.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/dresden/ll-ar.html">
ll-ar</a></td></tr>
<tr><td>Radial basis function fit</td>
<td><a href="dresden/rbf.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/dresden/rbf.html">rbf</a></tr>
<tr><td>Polynomial model</td>
<td><a href="dresden/polynom.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/dresden/polynom.html">polynom</a>,
<a href="dresden/polynomp.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/dresden/polynomp.html">polynomp</a>,
<a href="dresden/polyback.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/dresden/polyback.html">polyback</a>,
<a href="dresden/polypar.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/dresden/polypar.html">polypar</a></tr>
</table>
<h3><a name="noise">
Nonlinear noise reduction</a></h3>
This is how the three of us got into this business. Since spectral filters are
problematic with chaotic, broad band signals, new techniques were necessary.
All the implementations here use phase space projections for noise reduction.
The programs <a href="dresden/nrlazy.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/dresden/nrlazy.html">nrlazy</a> and
<a href="wuppertal/lazy.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/wuppertal/lazy.html">lazy</a> use locally
constant approximations of the dynamics. Rainers
<a href="dresden/nrlazy.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/dresden/nrlazy.html">nrlazy</a>
corrects the whole embedding vector, while Thomas'
<a href="wuppertal/lazy.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/wuppertal/lazy.html">lazy</a> corrects only the center point.
We haven't quite resolved yet which is preferable.
The two routines
<a href="dresden/ghkss.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/dresden/ghkss.html">ghkss</a> and
<a href="wuppertal/project.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/wuppertal/project.html">project</a> implement locally linear
projections (very similar).
Finally, for testing purposes you may want to add noise to data and compare
the outcome of your cleaning attempts with the true signal.
<p>
The <a href="chaospaper/node22.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/chaospaper/node22.html">introduction</a> paper has a section on
nonlinear noise reduction, too.
<p><table border>
<tr><td>Add noise to data</td>
<td><a href="dresden/makenoise.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/dresden/makenoise.html">makenoise</a>,
<a href="wuppertal/addnoise.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/wuppertal/addnoise.html">addnoise</a></td></tr>
<tr><td>Compare two data sets</td>
<td><a href="wuppertal/compare.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/wuppertal/compare.html">compare</a></td></tr>
<tr><td>Simple nonlinear noise reduction</td>
<td><a href="dresden/nrlazy.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/dresden/nrlazy.html">nrlazy</a>,
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