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<!--
 *
 * This help file was generated from arch_rnd.sci using help_from_sci().
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  <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>Syntax</title>
   <synopsis>
   y = 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>
This function simulates an ARCH sequence of length `t` with AR coefficients `b` and CH coefficients `a`.
The result `y(t)` follows the model:
y(t) = b(1) + b(2) * y(t-1) + … + b(lb) * y(t-lb+1) + e(t),
where `e(t)`, given `y` up to time `t-1`, is N(0, h(t)), with
h(t) = a(1) + a(2) * e(t-1)^2 + … + a(la) * e(t-la+1)^2.
   </para>
   <para>
</para>
</refsection>

<refsection>
   <title>Examples</title>
   <programlisting role="example"><![CDATA[
a = [1, 2, 3, 4, 5]
b = [7, 8, 9, 10]
t = 5
y = arch_rnd(a, b, t)

   ]]></programlisting>
</refsection>
</refentry>
