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arch_tes.m
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1999-12-24
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## Copyright (C) 1995, 1996, 1997 Kurt Hornik
##
## This program is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2, or (at your option)
## any later version.
##
## This program is distributed in the hope that it will be useful, but
## WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
## General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this file. If not, write to the Free Software Foundation,
## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
## usage: [pval, lm] = arch_tes (y, X, p)
## [pval, lm] = arch_tes (y, k, p)
##
## arch_tes (y, X, p) performs a Lagrange Multiplier (LM) test of the
## null hypothesis of no conditional heteroscedascity in the linear
## regression model y = X * b + e against the alternative of CH(p).
## I.e., the model is
## y(t) = b(1) * x(t,1) + ... + b(k) * x(t,k) + e(t),
## where given y up to t-1 and x up to t, e(t) is N(0, h(t)) with
## h(t) = v + a(1) * e(t-1)^2 + ... + a(p) * e(t-p)^2,
## and the null is a(1) == ... == a(p) == 0.
##
## arch_tes (y, k, p) does the same in a linear autoregression model of
## order k, i.e., with [1, y(t-1), ..., y(t-k)] as the t-th row of X.
##
## Under the null, lm approximately has a chisquare distribution with p
## degrees of freedom. pval is the p-value (1 minus the CDF of this
## distribution at lm) of the test.
##
## If no output argument is given, the p-value is displayed.
## Author: KH <Kurt.Hornik@ci.tuwien.ac.at>
## Description: Test for conditional heteroscedascity
function [pval, lm] = arch_tes (y, X, p)
if (nargin != 3)
error ("arch_tes needs 3 input arguments");
endif
if !(is_vec (y))
error ("arch_tes: y must be a vector");
endif
T = length (y);
y = reshape (y, T, 1);
[rx, cx] = size (X);
if ((rx == 1) && (cx == 1))
X = auto_mat (y, X);
elseif !(rx == T)
error (["arch_tes: ", ...
"either rows(X) == length(y), or X is a scalar"]);
endif
if !(is_scal(p) && (rem(p, 1) == 0) && (p > 0))
error ("arch_tes: p must be a positive integer.");
endif
[b, v_b, e] = ols (y, X);
Z = auto_mat (e.^2, p);
f = e.^2 / v_b - ones (T, 1);
f = Z' * f;
lm = f' * inv (Z'*Z) * f / 2;
pval = 1 - chi2_cdf (lm, p);
endfunction