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<?xml version="1.0" encoding="UTF-8"?>
<!--
*
* This help file was generated from arch_test.sci using help_from_sci().
*
-->
<refentry version="5.0-subset Scilab" xml:id="arch_test" xml:lang="en"
xmlns="http://docbook.org/ns/docbook"
xmlns:xlink="http://www.w3.org/1999/xlink"
xmlns:svg="http://www.w3.org/2000/svg"
xmlns:ns3="http://www.w3.org/1999/xhtml"
xmlns:mml="http://www.w3.org/1998/Math/MathML"
xmlns:scilab="http://www.scilab.org"
xmlns:db="http://docbook.org/ns/docbook">
<refnamediv>
<refname>arch_test</refname>
<refpurpose>perform a Lagrange Multiplier (LM) test of thenull hypothesis of no conditional heteroscedascity against the alternative of CH(P)</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>
arch_test(Y,X,P)
PVAL = arch_test(Y,X,P)
[PVAL, LM]= arch_test(Y,X,P)
</synopsis>
</refsynopsisdiv>
<refsection>
<title>Parameters</title>
<variablelist>
<varlistentry><term>P:</term>
<listitem><para> Degrees of freedom</para></listitem></varlistentry>
<varlistentry><term>PVAL:</term>
<listitem><para>PVAL is the p-value (1 minus the CDF of this distribution at LM) of the test</para></listitem></varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<para>
perform a Lagrange Multiplier (LM) test of thenull hypothesis of no conditional heteroscedascity against the alternative of CH(P).
</para>
<para>
I.e., the model is
</para>
<para>
y(t) = b(1) * x(t,1) + ... + b(k) * x(t,k) + e(t),
</para>
<para>
given Y up to t-1 and X up to t, e(t) is N(0, h(t)) with
</para>
<para>
h(t) = v + a(1) * e(t-1)^2 + ... + a(p) *e(t-p)^2, and the null is a(1) == ... == a(p) == 0.
</para>
<para>
If the second argument is a scalar integer, k,perform the sametest in a linear autoregression model of orderk, i.e., with
</para>
<para>
[1, y(t-1), ..., y(t-K)] as the t-th row of X.
</para>
<para>
Under the null, LM approximatel has a chisquare distribution with P degrees of freedom and PVAL is the p-value (1 minus the CDF of this distribution at LM) of the test.
</para>
<para>
If no output argument is given, the p-value is displayed.
</para>
</refsection>
</refentry>
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