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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_test (y, X, p)
+##         [pval, lm] = arch_test (y, k, p)
+##
+## arch_test (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_test (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_test (y, X, p)
+
+  if (nargin != 3)
+    error ("arch_test needs 3 input arguments");
+  endif
+
+  if !(is_vector (y))
+    error ("arch_test:  y must be a vector");
+  endif
+  T   = length (y);
+  y   = reshape (y, T, 1);
+  [rx, cx] = size (X);
+  if ((rx == 1) && (cx == 1))
+    X = autoreg_matrix (y, X);
+  elseif !(rx == T)
+    error (["arch_test:  ", ...
+	    "either rows(X) == length(y), or X is a scalar"]);
+  endif
+  if !(is_scalar(p) && (rem(p, 1) == 0) && (p > 0))
+    error ("arch_test:  p must be a positive integer.");
+  endif
+  
+  [b, v_b, e] = ols (y, X);
+  Z    = autoreg_matrix (e.^2, p);
+  f    = e.^2 / v_b - ones (T, 1);
+  f    = Z' * f;
+  lm   = f' * inv (Z'*Z) * f / 2;
+  pval = 1 - chisquare_cdf (lm, p);
+  
+endfunction
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