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<html> <head><title>Surrogate data testing</title></head><body bgcolor="#ffffff"><h3>Surrogate data testing</h3>A simple (one sided) surrogate data test for data in file <font color=blue><em>file</em></font>, usinga prediction error statistic, can be made with a sequence of commands similar to the following. First select a sub-sequence without large endpoint effect:<blockquote> <tt>></tt><font color=blue><tt> endtoend </tt> <em>file</em></font></blockquote>Suppose, the full data of length 1000 gave a 17% end effect, but a truncated length of 972 and offset 80 the effect was reduced to 0.2%. To choose thatsub-sequence: <blockquote> <tt>></tt><font color=blue><tt> choose -o selected.dat -x80 -l972 </tt> <em>file</em></font></blockquote>Here is the actual test:<blockquote> <tt>></tt><font color=blue><tt> surrogates -o -n19 selected.dat</tt></font> <br><tt>></tt><font color=blue><tt> predict -o -d1 -m3 -v0.1 selected.dat selected.dat_surr_??? | sort -nr</tt></font></blockquote>If the line of output corresponding to <font color=blue><tt>selected.dat</tt></font> is the last, the nullhypothesis of a stationary, possibly rescaled, linear Gaussian random processmay be rejected at the 95% level of significance, since the prediction error ofthe data is found to be smaller than that of the surrogates.<p>Or for a two sided test using time reversal symmetry statistic:<blockquote> <tt>></tt><font color=blue><tt> surrogates -n39 selected.dat</tt></font> <br><tt>></tt><font color=blue><tt> timerev -d1 selected.dat selected.dat_surr_??? | sort -nr</tt></font></blockquote>If the line of output corresponding to <font color=blue><tt>selected.dat</tt></font> is the last <font color=red>or</font>the first, the null hypothesis of a stationary, possibly rescaled, linearGaussian random process may be rejected at the 95% level of significance, sincethe time asymmetry of the data is found to be significantly different from that of the surrogates.<p>Test statistics can be derived from many of the programs given, includingprediction errors (<a href="predict.html">predict</a>), third order statistics(<a href="timerev.html">timerev</a>),correlation sums (<a href="c2.html">c2</a>), as well as unstable periodicorbits (<a href="upo.html">upo</a>).<p>Surrogate data are made by <a href="surrogates.html">surrogates</a>, or by aversion of <a href="randomize.html">randomize</a>.<p><a href="../contents.html">Table of Contents</a> * <a href="../../index.html" target="_top">TISEAN home</a></body></html>⌨️ 快捷键说明
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