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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>Model validation</TITLE><META NAME="description" CONTENT="Model validation"><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="tex2html245" HREF="node18.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="icons/next_motif.gif"></A> <A NAME="tex2html243" HREF="node16.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="icons/up_motif.gif"></A> <A NAME="tex2html237" HREF="node16.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="icons/previous_motif.gif"></A> <BR><B> Next:</B> <A NAME="tex2html246" HREF="node18.html">Simple nonlinear prediction</A><B>Up:</B> <A NAME="tex2html244" HREF="node16.html">Nonlinear prediction</A><B> Previous:</B> <A NAME="tex2html238" HREF="node16.html">Nonlinear prediction</A><BR> <P><H2><A NAME="SECTION00051000000000000000">Model validation</A></H2><P>Before entering the methods, we have to discuss how to assess the results. Themost obvious quantity for the quantification of predictability is the averageforecast error, i.e. the root of the mean squared (rms) deviation of theindividual prediction from the actual future value. If it is computed on thosevalues which were also used to construct the model (or to perform thepredictions), it is called the <I>in-sample error</I>. It is always advisableto save some data for an out-of-sample test. If the out-of-sample error isconsiderably larger than the in-sample error, data are either non-stationaryor one has overfitted the data, i.e. the fit extracted structure from randomfluctuations. A model with less parameters will then serve better. In caseswhere the data base is poor, on can apply <I>complete cross-validation</I> or<I>take-one-out statistics</I>, i.e. one constructs as many models as oneperforms forecasts, and in each case ignores the point one wants to predict.By construction, this method is realized in the local approaches, but not inthe global ones.<P>The most significant, but least quantitative way of model validation is toiterate the model and to compare this synthetic time series to theexperimental data. If they are compatible (e.g. in a delay plot), then themodel is likely to be reasonable. Quantitatively, it is not easy to define thecompatibility. One starts form an observed delay vector as intial condition,performs the first forecast, combines the forecast with all but the lastcomponents of the initial vector to a new delay vector, performs the nextforecast, and so on. The resulting time series should then be compared to themeasured data, most easily the attractor in a delay representation.<P><HR><A NAME="tex2html245" HREF="node18.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="icons/next_motif.gif"></A> <A NAME="tex2html243" HREF="node16.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="icons/up_motif.gif"></A> <A NAME="tex2html237" HREF="node16.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="icons/previous_motif.gif"></A> <BR><B> Next:</B> <A NAME="tex2html246" HREF="node18.html">Simple nonlinear prediction</A><B>Up:</B> <A NAME="tex2html244" HREF="node16.html">Nonlinear prediction</A><B> Previous:</B> <A NAME="tex2html238" HREF="node16.html">Nonlinear prediction</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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