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<html><head><title>Nonlinear Time Series Routines</title></head><body bgcolor="#ffffff"><h1 align=center><a name="top">TISEAN 3.0.1: Table of Contents</h1><center><font size=+1><a href="alphabetical.html">All programs in alphabetical order</a></font></center><h3 align=left>Sections</h3><ul><li><a href="#generating">Generating time series</a></li><li><a href="#linear">Linear tools</a></li><li><a href="#utilities">Utilities</a></li><li><a href="#visual">Stationarity</a></li><li><a href="#embedding">Embedding and Poincaré sections</a></li><li><a href="#prediction">Prediction</a></li><li><a href="#noise">Noise reduction</a></li><li><a href="#dimension">Dimension and entropy estimation</a></li><li><a href="#lyapunov">Lyapunov exponents</a></li><li><a href="#surrogates">Surrogate data</a></li><li><a href="#spike">Spike trains</a></li><li><a href="#xtisean">XTisean</a></li><li><a href="#unsupported">Unsupported</a></li></ul><h3 align=center><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 align=center border><tr><td>Create Hénon time series</td> <td><a href="docs_f/henon.html">henon</a></td></tr><tr><td>Create Ikeda time series</td> <td><a href="docs_f/ikeda.html">ikeda</a></td></tr><tr><td>Create Lorenz time series</td> <td><a href="docs_f/lorenz.html">lorenz</a></td></tr><tr><td>Run an 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></td></tr></table><a href="#top">Top</a><p><hr></p><h3 align=center><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 align=center 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>ARIMA model</td><td><a href="docs_c/arima-model.html">arima-model</a></td></tr><tr><td>Autocorrelation function</td> <td><a href="docs_c/corr.html">corr</a></tr><tr><td>Power spectrum using the maximum entropy method</td> <td><a href="docs_c/mem_spec.html">mem_spec</a></td></tr><tr><td>Power spectrum using FFT</td> <td> <a href="docs_f/spectrum.html">spectrum</a></td></tr><tr><td>Principal Component Analysis</td> <td><a href="docs_c/pca.html">pca</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><a href="#top">Top</a><p><hr></p><h3 align=center><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 align=center><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></table><a href="#top">Top</a><p><hr></p><h3 align=center><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 align=center><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><a href="#top">Top</a><p><hr></p><h3 align=center><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_c/delay.html">delay</a>. <p>Phase space reconstruction is discussed also in thethe <a href="chaospaper/node5.html">introduction</a> paper.<p><table border align=center><tr><td>Embed using delay coordinates</td> <td><a href="docs_c/delay.html">delay</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><a href="#top">Top</a><p><hr></p><h3 align=center><a name="prediction">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. Locallyzeroth order models, locally first order 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 align=center><tr><td>Locally zeroth order model test</td> <td><a href="docs_c/lzo-test.html">lzo-test</a></td></tr><tr><td>Iterate locally zeroth order model</td> <td><a href="docs_c/lzo-run.html">lzo-run</a></td></tr><tr><td>Locally first order model test</td><td><a href="docs_c/lfo-test.html">lfo-test</td></tr><tr><td>Iterate locally first order model</td> <td><a href="docs_c/lfo-run.html">lfo-run</a></td></tr><tr><td>Local vs. global linear prediction</td> <td><a href="docs_c/lfo-ar.html"> lfo-ar</a></td></tr><tr><td>Local vs. global mean prediction</td><td><a href="docs_c/lzo-gm.html">lzo-gm</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><a href="#top">Top</a><p><hr></p><h3 align=center><a name="noise">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 program<a href="docs_f/lazy.html">lazy</a> use locallyconstant approximations of the dynamics. The routine<a href="docs_c/ghkss.html">ghkss</a> implements locally linearprojections.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 align=center><tr><td>Add noise to data</td> <td><a href="docs_c/makenoise.html">makenoise</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>⌨️ 快捷键说明
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