1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
|
<?xml version="1.0" encoding="UTF-8"?>
<!--
*
* This help file was generated from arch_fit.sci using help_from_sci().
*
-->
<refentry version="5.0-subset Scilab" xml:id="arch_fit" 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_fit</refname>
<refpurpose>This functions fits an ARCH regression model to the time series Y using the scoring algorithm in Engle's original ARCH paper.</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>
[A, B] = arch_fit (Y, X, P, ITER, GAMMA, A0, B0)
</synopsis>
</refsynopsisdiv>
<refsection>
<title>Parameters</title>
<variablelist>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<para>
Fit an ARCH regression model to the time series Y using the scoring algorithm in Engle's original ARCH paper.
</para>
<para>
The model is
</para>
<para>
y(t) = b(1) * x(t,1) + ... + b(k) * x(t,k) + e(t),
h(t) = a(1) + a(2) * e(t-1)^2 + ... + a(p+1) * e(t-p)^2
</para>
<para>
in which e(t) is N(0, h(t)), given a time-series vector Y up to time t-1 and a matrix of (ordinary) regressors X up to t. The order of the regression of the residual variance is specified by P.
</para>
<para>
If invoked as 'arch_fit (Y, K, P)' with a positive integer K, fit an ARCH(K, P) process, i.e., do the above with the t-th row of X given by
</para>
<para>
[1, y(t-1), ..., y(t-k)]
</para>
<para>
Optionally, one can specify the number of iterations ITER, the updating factor GAMMA, and initial values a0 and b0 for the scoring algorithm.
</para>
</refsection>
</refentry>
|
