update packages

[CreaPhase.git] / octave_packages / m / signal / arch_test.m

diff --git a/octave_packages/m/signal/arch_test.m b/octave_packages/m/signal/arch_test.m
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+## Copyright (C) 1995-2012 Kurt Hornik
+##
+## This file is part of Octave.
+##
+## Octave 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 3 of the License, or (at
+## your option) any later version.
+##
+## Octave 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 Octave; see the file COPYING.  If not, see
+## <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {[@var{pval}, @var{lm}] =} arch_test (@var{y}, @var{x}, @var{p})
+## For a linear regression model
+##
+## @example
+## y = x * b + e
+## @end example
+##
+## @noindent
+## perform a Lagrange Multiplier (LM) test of the null hypothesis of no
+## conditional heteroscedascity against the alternative of CH(@var{p}).
+##
+## I.e., the model is
+##
+## @example
+## y(t) = b(1) * x(t,1) + @dots{} + b(k) * x(t,k) + e(t),
+## @end example
+##
+## @noindent
+## given @var{y} up to @math{t-1} and @var{x} up to @math{t},
+## @math{e}(t) is @math{N(0, h(t))} with
+##
+## @example
+## h(t) = v + a(1) * e(t-1)^2 + @dots{} + a(p) * e(t-p)^2,
+## @end example
+##
+## @noindent
+## and the null is @math{a(1)} == @dots{} == @math{a(p)} == 0.
+##
+## If the second argument is a scalar integer, @math{k}, perform the same
+## test in a linear autoregression model of order @math{k}, i.e., with
+##
+## @example
+## [1, y(t-1), @dots{}, y(t-@var{k})]
+## @end example
+##
+## @noindent
+## as the @math{t}-th row of @var{x}.
+##
+## Under the null, LM approximately has a chisquare distribution with
+## @var{p} degrees of freedom and @var{pval} is the @math{p}-value (1
+## minus the CDF of this distribution at LM) of the test.
+##
+## If no output argument is given, the @math{p}-value is displayed.
+## @end deftypefn
+
+## Author: KH <Kurt.Hornik@wu-wien.ac.at>
+## Description: Test for conditional heteroscedascity
+
+function [pval, lm] = arch_test (y, x, p)
+
+  if (nargin != 3)
+    error ("arch_test: 3 input arguments required");
+  endif
+
+  if (! (isvector (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 (! (isscalar(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 - chi2cdf (lm, p);
+
+endfunction