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<!--
 *
 * This help file was generated from arma_rnd.sci using help_from_sci().
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  <refnamediv>
    <refname>arma_rnd</refname>
    <refpurpose>Return a simulation of the ARMA model.</refpurpose>
  </refnamediv>


<refsynopsisdiv>
   <title>Syntax</title>
   <synopsis>
   x = arma_rnd(a, b, v, t, n)
   x = arma_rnd(a, b, v, t)
   
   </synopsis>
</refsynopsisdiv>

<refsection>
   <title>Parameters</title>
   <variablelist>
        <varlistentry>
            <term>a:</term>
            <listitem><para> Real vector. Coefficients of the autoregressive (AR) part of the model.</para></listitem>
        </varlistentry>
        <varlistentry>
            <term>b:</term>
            <listitem><para> Real vector. Coefficients of the moving average (MA) part of the model.</para></listitem>
        </varlistentry>
        <varlistentry>
            <term>v:</term>
            <listitem><para> Variance of the Gaussian white noise.</para></listitem>
        </varlistentry>
        <varlistentry>
            <term>t:</term>
            <listitem><para> Length of the output vector.</para></listitem>
        </varlistentry>
        <varlistentry>
            <term>n:</term>
            <listitem><para> Number of dummy x(i) used for initialization (optional, default = 100).</para></listitem>
        </varlistentry>
   </variablelist>
</refsection>

<refsection>
   <title>Description</title>
   <para>
The ARMA model is defined by:
x(n) = a(1) * x(n-1) + … + a(k) * x(n-k) + e(n) + b(1) * e(n-1) + … + b(l) * e(n-l),
where `k` is the length of vector `a`, `l` is the length of vector `b`, and `e` is Gaussian white noise with variance `v`.
The function returns a vector of length `t`. The optional parameter `n` specifies the number of dummy x(i) used for initialization.
If `n` is omitted, it defaults to 100.
   </para>
   <para>
</para>
</refsection>

<refsection>
   <title>Examples</title>
   <programlisting role="example"><![CDATA[
a = [1, 2, 3, 4, 5]
b = [7, 8, 9, 10, 11]
v = 10
t = 5
n = 100
x = arma_rnd(a, b, v, t, n)

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