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<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML 2.2//EN"><!--Converted with LaTeX2HTML 96.1-h (September 30, 1996) by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds --><HTML><HEAD><TITLE>Testing for nonlinearity</TITLE><META NAME="description" CONTENT="Testing for nonlinearity"><META NAME="keywords" CONTENT="TiseanHTML"><META NAME="resource-type" CONTENT="document"><META NAME="distribution" CONTENT="global"><LINK REL=STYLESHEET HREF="TiseanHTML.css"></HEAD><BODY bgcolor=ffffff LANG="EN" > <A NAME="tex2html426" HREF="node36.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="icons/next_motif.gif"></A> <A NAME="tex2html424" HREF="TiseanHTML.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="icons/up_motif.gif"></A> <A NAME="tex2html418" HREF="node34.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="icons/previous_motif.gif"></A> <BR><B> Next:</B> <A NAME="tex2html427" HREF="node36.html">The concept of surrogate </A><B>Up:</B> <A NAME="tex2html425" HREF="TiseanHTML.html">Practical implementation of nonlinear </A><B> Previous:</B> <A NAME="tex2html419" HREF="node34.html">Entropy estimates</A><BR> <P><H1><A NAME="SECTION00090000000000000000">Testing for nonlinearity</A></H1><A NAME="secsurro"> </A>Most of the methods and quantities discussed so far are most appropriate incases where the data show strong and consistent nonlinear deterministicsignatures. As soon as more than a small or at most moderate amount ofadditive noise is present, scaling behavior will be broken and predictabilitywill be limited. Thus we have explored the opposite extreme, nonlinear andfully deterministic, rather than the classical linear stochastic processes.The bulk of real world time series falls in neither of these limitingcategories because they reflect nonlinear responses and effectively stochasticcomponents at the same time. Little can be done for many of these cases withcurrent methods. Often it will be advisable to take advantage of thewell founded machinery of spectral methods and venture into nonlinearterritory only if encouraged by positive evidence. This section is aboutmethods to establish statistical evidence for nonlinearity beyond a simplerescaling in a time series.<P><BR> <HR><UL><A NAME="CHILD_LINKS"> </A><LI> <A NAME="tex2html428" HREF="node36.html#SECTION00091000000000000000">The concept of surrogate data</A><LI> <A NAME="tex2html429" HREF="node37.html#SECTION00092000000000000000">Iterative Fourier transform method</A><LI> <A NAME="tex2html430" HREF="node38.html#SECTION00093000000000000000">General constrained randomization</A><LI> <A NAME="tex2html431" HREF="node39.html#SECTION00094000000000000000">Measuring weak nonlinearity</A></UL><HR><A NAME="tex2html426" HREF="node36.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="icons/next_motif.gif"></A> <A NAME="tex2html424" HREF="TiseanHTML.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="icons/up_motif.gif"></A> <A NAME="tex2html418" HREF="node34.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="icons/previous_motif.gif"></A> <BR><B> Next:</B> <A NAME="tex2html427" HREF="node36.html">The concept of surrogate </A><B>Up:</B> <A NAME="tex2html425" HREF="TiseanHTML.html">Practical implementation of nonlinear </A><B> Previous:</B> <A NAME="tex2html419" HREF="node34.html">Entropy estimates</A><P><ADDRESS><I>Thomas Schreiber <BR>Wed Jan 6 15:38:27 CET 1999</I></ADDRESS></BODY></HTML>⌨️ 快捷键说明
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