Mercurial > octave-nkf
annotate scripts/signal/arch_test.m @ 16033:23a7661e529a ss-3-7-2
snapshot version 3.7.2
* configure.ac (AC_INIT): Set version to 3.7.2.
(OCTAVE_RELEASE_DATE): Set to 2013-02-09.
(OCTAVE_COPYRIGHT): Update year.
| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Sun, 10 Feb 2013 00:59:19 -0500 |
| parents | 5d3a684236b0 |
| children | 1c89599167a6 |
| rev | line source |
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1 ## Copyright (C) 1995-2012 Kurt Hornik |
| 3426 | 2 ## |
| 3922 | 3 ## This file is part of Octave. |
| 4 ## | |
| 5 ## Octave is free software; you can redistribute it and/or modify it | |
| 6 ## under the terms of the GNU General Public License as published by | |
| 7016 | 7 ## the Free Software Foundation; either version 3 of the License, or (at |
| 8 ## your option) any later version. | |
| 3426 | 9 ## |
| 3922 | 10 ## Octave is distributed in the hope that it will be useful, but |
| 3191 | 11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
| 12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 3426 | 13 ## General Public License for more details. |
| 14 ## | |
| 3191 | 15 ## You should have received a copy of the GNU General Public License |
| 7016 | 16 ## along with Octave; see the file COPYING. If not, see |
| 17 ## <http://www.gnu.org/licenses/>. | |
| 3191 | 18 |
| 3449 | 19 ## -*- texinfo -*- |
| 3909 | 20 ## @deftypefn {Function File} {[@var{pval}, @var{lm}] =} arch_test (@var{y}, @var{x}, @var{p}) |
| 3449 | 21 ## For a linear regression model |
| 3191 | 22 ## |
| 3449 | 23 ## @example |
| 24 ## y = x * b + e | |
| 25 ## @end example | |
| 26 ## | |
| 27 ## @noindent | |
| 28 ## perform a Lagrange Multiplier (LM) test of the null hypothesis of no | |
| 29 ## conditional heteroscedascity against the alternative of CH(@var{p}). | |
| 30 ## | |
| 3191 | 31 ## I.e., the model is |
| 3449 | 32 ## |
| 33 ## @example | |
| 3499 | 34 ## y(t) = b(1) * x(t,1) + @dots{} + b(k) * x(t,k) + e(t), |
| 3449 | 35 ## @end example |
| 36 ## | |
| 37 ## @noindent | |
| 3499 | 38 ## given @var{y} up to @math{t-1} and @var{x} up to @math{t}, |
| 39 ## @math{e}(t) is @math{N(0, h(t))} with | |
| 3449 | 40 ## |
| 41 ## @example | |
| 3499 | 42 ## h(t) = v + a(1) * e(t-1)^2 + @dots{} + a(p) * e(t-p)^2, |
| 3449 | 43 ## @end example |
| 44 ## | |
| 45 ## @noindent | |
| 3499 | 46 ## and the null is @math{a(1)} == @dots{} == @math{a(p)} == 0. |
| 3191 | 47 ## |
| 3499 | 48 ## If the second argument is a scalar integer, @math{k}, perform the same |
| 49 ## test in a linear autoregression model of order @math{k}, i.e., with | |
| 3449 | 50 ## |
| 51 ## @example | |
| 3499 | 52 ## [1, y(t-1), @dots{}, y(t-@var{k})] |
| 3449 | 53 ## @end example |
| 3191 | 54 ## |
| 3449 | 55 ## @noindent |
| 3499 | 56 ## as the @math{t}-th row of @var{x}. |
| 3191 | 57 ## |
| 3449 | 58 ## Under the null, LM approximately has a chisquare distribution with |
| 3499 | 59 ## @var{p} degrees of freedom and @var{pval} is the @math{p}-value (1 |
| 3449 | 60 ## minus the CDF of this distribution at LM) of the test. |
| 61 ## | |
| 3499 | 62 ## If no output argument is given, the @math{p}-value is displayed. |
| 3449 | 63 ## @end deftypefn |
| 3426 | 64 |
| 5428 | 65 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
| 3457 | 66 ## Description: Test for conditional heteroscedascity |
| 3426 | 67 |
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68 function [pval, lm] = arch_test (y, x, p) |
| 3191 | 69 |
| 70 if (nargin != 3) | |
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71 error ("arch_test: 3 input arguments required"); |
| 3191 | 72 endif |
| 73 | |
| 4030 | 74 if (! (isvector (y))) |
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75 error ("arch_test: Y must be a vector"); |
| 3191 | 76 endif |
| 77 T = length (y); | |
| 78 y = reshape (y, T, 1); | |
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79 [rx, cx] = size (x); |
| 3191 | 80 if ((rx == 1) && (cx == 1)) |
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81 x = autoreg_matrix (y, x); |
| 3457 | 82 elseif (! (rx == T)) |
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83 error ("arch_test: either rows (X) == length (Y), or X is a scalar"); |
| 3191 | 84 endif |
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85 if (! (isscalar (p) && (rem (p, 1) == 0) && (p > 0))) |
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86 error ("arch_test: P must be a positive integer"); |
| 3191 | 87 endif |
| 3426 | 88 |
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89 [b, v_b, e] = ols (y, x); |
| 3191 | 90 Z = autoreg_matrix (e.^2, p); |
| 91 f = e.^2 / v_b - ones (T, 1); | |
| 92 f = Z' * f; | |
| 93 lm = f' * inv (Z'*Z) * f / 2; | |
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94 pval = 1 - chi2cdf (lm, p); |
| 3426 | 95 |
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96 endfunction |