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<html><head><title>Nonlinear Time Series Routines</title></head><body bgcolor="#ffffff"><h1>TISEAN 2.1: Table of Contents</h1><h3><a name="generating">Generating time series</a></h3>A few routines are provided to generate test data from simpleequations. Since there are powerfull packages (for example <ahref="http://keck2.umd.edu/dynamics/">Dynamics</a> by Helena Nusse and JimYorke) 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="docs_f/henon.html">henon</a></td></tr><tr><td>Make Ikeda time series</td> <td><a href="docs_f/ikeda.html">ikeda</a></td></tr><tr><td>Run autoregressive model</td> <td><a href="docs_f/ar-run.html">ar-run</a></td></tr><tr><td>Add noise to data</td> <td><a href="docs_c/makenoise.html">makenoise</a>, <a href="docs_f/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 seriesmethods which are there just for convenience. If you want to embark seriouslyon linear or spectral analysis of your data, you will have to use any one ofthe statistical or mathematics packages around. Please, don't judge us by thelevel of sophistication in this section!<p><table border><tr><td>AR model</td> <td><a href="docs_c/ar-model.html">ar-model</a>, <a href="docs_f/ar-run.html">ar-run</a></td></tr><tr><td>Autocorrelation function</td> <td><a href="docs_c/corr.html">corr</a>, <a href="docs_f/autocor.html">autocor</a></td></tr><tr><td>Autocorrelation function of event times</td> <td><a href="docs_f/spikeauto.html">spikeauto</a></td></tr><tr><td>Power spectrum</td> <td><a href="docs_c/mem_spec.html">mem_spec</a>, <a href="docs_f/spectrum.html">spectrum</a></td></tr><tr><td>Power spectrum of event times</td> <td><a href="docs_f/spikespec.html">spikespec</a></td></tr><tr><td>Notch filter</td> <td><a href="docs_f/notch.html">notch</a></td></tr><tr><td>Wiener filter</td> <td><a href="docs_f/wiener.html">wiener</a></td></tr><tr><td>Simple low pass filter</td> <td><a href="docs_c/low121.html">low121</a></tr><tr><td>Savitzky-Golay filter</td> <td><a href="docs_c/sav_gol.html">sav_gol</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 ofwriting your own five-line Perl, awk, FORTRAN or C programs.<p><table border><tr><td>Choose sub-sequence or columns</td> <td><a href="docs_f/choose.html">choose</a></td></tr><tr><td>Normalise, rescale, mean, standard deviation</td> <td><a href="docs_c/rescale.html">rescale</a>, <a href="docs_f/rms.html">rms</a></td></tr> <tr><td>Distribution of the data</td> <td><a href="docs_c/histogram.html">histogram</a></td></tr> <tr><td>Change sampling time</td> <td><a href="docs_c/resample.html">resample</a></tr><tr><td>Event/intervcal conversion</td> <td><a href="docs_f/intervals.html">intervals</a></td></tr><tr><td>Interval/event conversion</td> <td><a href="docs_f/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 seriesproperties and another stationarity test as proposed by <ahref="chaospaper/citation.html#statio">Schreiber</a>. The recurrence plotand the space time separation plot are of great value for the detection ofnonstationarity, selection of relevant time scales, selection of stationaryepisodes and so forth.<p>There is a short corresponding section in the <a href="chaospaper/node13.html">introduction</a> paper.<p><table border><tr><td>Recurrence plot</td> <td><a href="docs_c/recurr.html">recurr</a></td></tr><tr><td>Space-time separation plot</td> <td><a href="docs_f/stp.html">stp</a></td></tr><tr><td>Stationarity test</td> <td><a href="docs_c/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 nonlinearmethods 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 ofparameters, etc. For delay embeddings, use<a href="docs_f/delay.html">delay</a>. For principal components,<a href="docs_c/svd.html">svd</a> and<a href="docs_f/pc.html">pc</a> do almost the same thing.<p>Phase space reconstruction is discussed also in thethe <a href="chaospaper/node5.html">introduction</a> paper.<p><table border><tr><td>Embed using delay coordinates</td> <td><a href="docs_f/delay.html">delay</a></td></tr><tr><td>Embed using principal components</td> <td><a href="docs_c/svd.html">svd</a>, <a href="docs_f/pc.html">pc</a></td></tr><tr><td>Mutual information of the data</td> <td><a href="docs_c/mutual.html">mutual</a></tr><tr><td>Poincaré section</td> <td><a href="docs_c/poincare.html">poincare</a></tr><tr><td>Determine the extrema of a time series</td> <td><a href="docs_c/extrema.html">extrema</a></tr><tr><td>Unstable periodic orbits</td> <td> <a href="docs_f/upo.html">upo</a>, <a href="docs_f/upoembed.html">upoembed</a></td></tr><tr><td>False nearest neighbours</td> <td><a href="docs_c/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 similarprograms <a href="docs_c/zeroth.html">zeroth</a> and<a href="docs_f/predict.html">predict</a> use locally constant fits.This is the most robust approach for short, noisy signals, easy handling andquick answers. Further, local linear models, radial basis functions, andpolynomial fits are provided.<p>For a discussion of these methods and examples see the corresponding section ofthe <a href="chaospaper/node16.html">introduction</a> paper.<p><table border><tr><td>Simple nonlinear prediction</td> <td><a href="docs_c/zeroth.html">zeroth</a>, <a href="docs_f/predict.html">predict</a></td></tr><tr><td>Local linear model</td> <td><a href="docs_c/onestep.html">onestep</a>, <a href="docs_c/nstep.html">nstep</a></tr><tr><td>Local vs. global linear prediction</td> <td><a href="docs_c/ll-ar.html"> ll-ar</a></td></tr><tr><td>Radial basis function fit</td> <td><a href="docs_c/rbf.html">rbf</a></tr><tr><td>Polynomial model</td> <td><a href="docs_c/polynom.html">polynom</a>, <a href="docs_c/polynomp.html">polynomp</a>, <a href="docs_c/polyback.html">polyback</a>, <a href="docs_c/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 areproblematic with chaotic, broad band signals, new techniques were necessary.All the implementations here use phase space projections for noise reduction.The programs <a href="docs_c/nrlazy.html">nrlazy</a> and<a href="docs_f/lazy.html">lazy</a> use locallyconstant approximations of the dynamics. Rainers <a href="docs_c/nrlazy.html">nrlazy</a> corrects the whole embedding vector, while Thomas' <a href="docs_f/lazy.html">lazy</a> corrects only the center point.We haven't quite resolved yet which is preferable.The two routines<a href="docs_c/ghkss.html">ghkss</a> and <a href="docs_f/project.html">project</a> implement locally linearprojections (very similar).Finally, for testing purposes you may want to add noise to data and comparethe outcome of your cleaning attempts with the true signal.<p>The <a href="chaospaper/node22.html">introduction</a> paper has a section onnonlinear noise reduction, too.<p><table border><tr><td>Add noise to data</td> <td><a href="docs_c/makenoise.html">makenoise</a>, <a href="docs_f/addnoise.html">addnoise</a></td></tr><tr><td>Compare two data sets</td> <td><a href="docs_f/compare.html">compare</a></td></tr><tr><td>Simple nonlinear noise reduction</td> <td><a href="docs_c/nrlazy.html">nrlazy</a>, <a href="docs_f/lazy.html">lazy</a></td></tr><tr><td>Nonlinear noise reduction</td> <td><a href="docs_c/ghkss.html">ghkss</a>, <a href="docs_f/project.html">project</a></td></tr></table><h3><a name="dimension">Dimension and entropy estimation</a></h3>⌨️ 快捷键说明
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