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<?xml version="1.0" encoding="UTF-8"?>
<!--
*
* This help file was generated from arch_rnd.sci using help_from_sci().
*
-->
<refentry version="5.0-subset Scilab" xml:id="arch_rnd" 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_rnd</refname>
<refpurpose>Simulate an ARCH sequence of length t with AR coefficients b and CH coefficients a.</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>
arch_rnd (a, b, t)
</synopsis>
</refsynopsisdiv>
<refsection>
<title>Parameters</title>
<variablelist>
<varlistentry><term>a:</term>
<listitem><para> CH coefficients</para></listitem></varlistentry>
<varlistentry><term>b:</term>
<listitem><para> AR coefficients</para></listitem></varlistentry>
<varlistentry><term>t:</term>
<listitem><para> Length of ARCH sequence</para></listitem></varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<para>
It Simulates an ARCH sequence of length t with AR coefficients b and CH coefficients a.
The result y(t) follows the model
</para>
<para>
<latex>
\begin{eqnarray}
y(t) = b(1) + b(2) * y(t-1) + … + b(lb) * y(t-lb+1) + e(t)
\end{eqnarray}
</latex>
<para>
where e(t), given y up to time t-1, is N(0, h(t)), with
</para>
</para>
<para>
<latex>
\begin{eqnarray}
h(t) = a(1) + a(2) * e(t-1)^2 + … + a(la) * e(t-la+1)^2
\end{eqnarray}
</latex>
</para>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
a = [1 2 3 4 5];
b = [7 8 9 10];
t = 5 ;
arch_rnd (a, b, t)
]]></programlisting>
</refsection>
</refentry>
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