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1 ## Copyright (C) 1995, 1996, 1997 Kurt Hornik |
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2 ## |
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3 ## This file is part of Octave. |
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4 ## |
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5 ## Octave is free software; you can redistribute it and/or modify it |
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6 ## under the terms of the GNU General Public License as published by |
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7 ## the Free Software Foundation; either version 2, or (at your option) |
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8 ## any later version. |
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9 ## |
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10 ## Octave is distributed in the hope that it will be useful, but |
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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13 ## General Public License for more details. |
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14 ## |
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15 ## You should have received a copy of the GNU General Public License |
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16 ## along with Octave; see the file COPYING. If not, write to the Free |
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17 ## Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |
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18 ## 02110-1301, USA. |
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19 |
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20 ## -*- texinfo -*- |
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21 ## @deftypefn {Function File} {[@var{pval}, @var{lm}] =} arch_test (@var{y}, @var{x}, @var{p}) |
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22 ## For a linear regression model |
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23 ## |
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24 ## @example |
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25 ## y = x * b + e |
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26 ## @end example |
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27 ## |
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28 ## @noindent |
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29 ## perform a Lagrange Multiplier (LM) test of the null hypothesis of no |
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30 ## conditional heteroscedascity against the alternative of CH(@var{p}). |
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31 ## |
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32 ## I.e., the model is |
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33 ## |
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34 ## @example |
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35 ## y(t) = b(1) * x(t,1) + @dots{} + b(k) * x(t,k) + e(t), |
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36 ## @end example |
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37 ## |
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38 ## @noindent |
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39 ## given @var{y} up to @math{t-1} and @var{x} up to @math{t}, |
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40 ## @math{e}(t) is @math{N(0, h(t))} with |
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41 ## |
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42 ## @example |
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43 ## h(t) = v + a(1) * e(t-1)^2 + @dots{} + a(p) * e(t-p)^2, |
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44 ## @end example |
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45 ## |
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46 ## @noindent |
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47 ## and the null is @math{a(1)} == @dots{} == @math{a(p)} == 0. |
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48 ## |
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49 ## If the second argument is a scalar integer, @math{k}, perform the same |
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50 ## test in a linear autoregression model of order @math{k}, i.e., with |
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51 ## |
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52 ## @example |
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53 ## [1, y(t-1), @dots{}, y(t-@var{k})] |
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54 ## @end example |
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55 ## |
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56 ## @noindent |
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57 ## as the @math{t}-th row of @var{x}. |
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58 ## |
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59 ## Under the null, LM approximately has a chisquare distribution with |
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60 ## @var{p} degrees of freedom and @var{pval} is the @math{p}-value (1 |
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61 ## minus the CDF of this distribution at LM) of the test. |
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62 ## |
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63 ## If no output argument is given, the @math{p}-value is displayed. |
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64 ## @end deftypefn |
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65 |
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66 ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at> |
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67 ## Description: Test for conditional heteroscedascity |
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68 |
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69 function [pval, lm] = arch_test (y, X, p) |
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70 |
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71 if (nargin != 3) |
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72 error ("arch_test needs 3 input arguments"); |
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73 endif |
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74 |
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75 if (! (isvector (y))) |
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76 error ("arch_test: y must be a vector"); |
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77 endif |
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78 T = length (y); |
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79 y = reshape (y, T, 1); |
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80 [rx, cx] = size (X); |
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81 if ((rx == 1) && (cx == 1)) |
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82 X = autoreg_matrix (y, X); |
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83 elseif (! (rx == T)) |
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84 error ("arch_test: either rows(X) == length(y), or X is a scalar"); |
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85 endif |
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86 if (! (isscalar(p) && (rem(p, 1) == 0) && (p > 0))) |
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87 error ("arch_test: p must be a positive integer"); |
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88 endif |
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89 |
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90 [b, v_b, e] = ols (y, X); |
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91 Z = autoreg_matrix (e.^2, p); |
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92 f = e.^2 / v_b - ones (T, 1); |
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93 f = Z' * f; |
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94 lm = f' * inv (Z'*Z) * f / 2; |
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95 pval = 1 - chisquare_cdf (lm, p); |
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96 |
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97 endfunction |
