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1 ## Copyright (C) 1995, 1996, 1997 Kurt Hornik |
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2 ## |
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3 ## This program is free software; you can redistribute it and/or modify |
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4 ## it under the terms of the GNU General Public License as published by |
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5 ## the Free Software Foundation; either version 2, or (at your option) |
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6 ## any later version. |
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7 ## |
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8 ## This program is distributed in the hope that it will be useful, but |
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9 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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10 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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11 ## General Public License for more details. |
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12 ## |
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13 ## You should have received a copy of the GNU General Public License |
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14 ## along with this file. If not, write to the Free Software Foundation, |
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15 ## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
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16 |
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17 ## -*- texinfo -*- |
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18 ## @deftypefn {Function File} {} {[@var{pval}, @var{lm}] =} arch_test (@var{y}, @var{x}, @var{p}) |
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19 ## For a linear regression model |
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20 ## |
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21 ## @example |
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22 ## y = x * b + e |
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23 ## @end example |
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24 ## |
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25 ## @noindent |
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26 ## perform a Lagrange Multiplier (LM) test of the null hypothesis of no |
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27 ## conditional heteroscedascity against the alternative of CH(@var{p}). |
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28 ## |
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29 ## I.e., the model is |
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30 ## |
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31 ## @example |
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32 ## y(t) = b(1) * x(t,1) + @dots{} + b(k) * x(t,k) + e(t), |
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33 ## @end example |
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34 ## |
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35 ## @noindent |
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36 ## given @var{y} up to @math{t-1} and @var{x} up to @math{t}, |
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37 ## @math{e}(t) is @math{N(0, h(t))} with |
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38 ## |
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39 ## @example |
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40 ## h(t) = v + a(1) * e(t-1)^2 + @dots{} + a(p) * e(t-p)^2, |
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41 ## @end example |
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42 ## |
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43 ## @noindent |
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44 ## and the null is @math{a(1)} == @dots{} == @math{a(p)} == 0. |
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45 ## |
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46 ## If the second argument is a scalar integer, @math{k}, perform the same |
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47 ## test in a linear autoregression model of order @math{k}, i.e., with |
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48 ## |
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49 ## @example |
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50 ## [1, y(t-1), @dots{}, y(t-@var{k})] |
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51 ## @end example |
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52 ## |
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53 ## @noindent |
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54 ## as the @math{t}-th row of @var{x}. |
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55 ## |
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56 ## Under the null, LM approximately has a chisquare distribution with |
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57 ## @var{p} degrees of freedom and @var{pval} is the @math{p}-value (1 |
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58 ## minus the CDF of this distribution at LM) of the test. |
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59 ## |
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60 ## If no output argument is given, the @math{p}-value is displayed. |
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61 ## @end deftypefn |
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62 |
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63 ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at> |
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64 ## Description: Test for conditional heteroscedascity |
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65 |
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66 function [pval, lm] = arch_test (y, X, p) |
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67 |
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68 if (nargin != 3) |
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69 error ("arch_test needs 3 input arguments"); |
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70 endif |
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71 |
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72 if (! (is_vector (y))) |
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73 error ("arch_test: y must be a vector"); |
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74 endif |
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75 T = length (y); |
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76 y = reshape (y, T, 1); |
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77 [rx, cx] = size (X); |
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78 if ((rx == 1) && (cx == 1)) |
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79 X = autoreg_matrix (y, X); |
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80 elseif (! (rx == T)) |
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81 error ("arch_test: either rows(X) == length(y), or X is a scalar"); |
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82 endif |
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83 if (! (is_scalar(p) && (rem(p, 1) == 0) && (p > 0))) |
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84 error ("arch_test: p must be a positive integer"); |
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85 endif |
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86 |
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87 [b, v_b, e] = ols (y, X); |
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88 Z = autoreg_matrix (e.^2, p); |
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89 f = e.^2 / v_b - ones (T, 1); |
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90 f = Z' * f; |
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91 lm = f' * inv (Z'*Z) * f / 2; |
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92 pval = 1 - chisquare_cdf (lm, p); |
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93 |
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94 endfunction |
