Mercurial > hg > octave-nkf
annotate scripts/signal/arch_fit.m @ 14348:95c43fc8dbe1 stable rc-3-6-1-0
3.6.1 release candidate 0
* configure.ac (AC_INIT): Version is now 3.6.1-rc0.
(OCTAVE_RELEASE_DATE): Now 2012-02-07.
* liboctave/Makefile.am: Bump liboctave revision version.
* src/Makefile.am: Bump liboctave revision version.
| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Thu, 09 Feb 2012 11:25:04 -0500 |
| parents | 72c96de7a403 |
| children | 5d3a684236b0 |
| 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 -*- |
| 20 ## @deftypefn {Function File} {[@var{a}, @var{b}] =} arch_fit (@var{y}, @var{x}, @var{p}, @var{iter}, @var{gamma}, @var{a0}, @var{b0}) | |
| 21 ## Fit an ARCH regression model to the time series @var{y} using the | |
| 22 ## scoring algorithm in Engle's original ARCH paper. The model is | |
| 3191 | 23 ## |
| 3449 | 24 ## @example |
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25 ## @group |
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26 ## y(t) = b(1) * x(t,1) + @dots{} + b(k) * x(t,k) + e(t), |
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27 ## h(t) = a(1) + a(2) * e(t-1)^2 + @dots{} + a(p+1) * e(t-p)^2 |
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28 ## @end group |
| 3449 | 29 ## @end example |
| 3191 | 30 ## |
| 3449 | 31 ## @noindent |
| 3499 | 32 ## in which @math{e(t)} is @math{N(0, h(t))}, given a time-series vector |
| 33 ## @var{y} up to time @math{t-1} and a matrix of (ordinary) regressors | |
| 34 ## @var{x} up to @math{t}. The order of the regression of the residual | |
| 35 ## variance is specified by @var{p}. | |
| 3191 | 36 ## |
| 3449 | 37 ## If invoked as @code{arch_fit (@var{y}, @var{k}, @var{p})} with a |
| 38 ## positive integer @var{k}, fit an ARCH(@var{k}, @var{p}) process, | |
| 3499 | 39 ## i.e., do the above with the @math{t}-th row of @var{x} given by |
| 3191 | 40 ## |
| 3449 | 41 ## @example |
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42 ## [1, y(t-1), @dots{}, y(t-k)] |
| 3449 | 43 ## @end example |
| 44 ## | |
| 45 ## Optionally, one can specify the number of iterations @var{iter}, the | |
| 3499 | 46 ## updating factor @var{gamma}, and initial values @math{a0} and |
| 47 ## @math{b0} for the scoring algorithm. | |
| 3449 | 48 ## @end deftypefn |
| 3191 | 49 |
| 5428 | 50 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
| 3457 | 51 ## Description: Fit an ARCH regression model |
| 3191 | 52 |
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53 function [a, b] = arch_fit (y, x, p, iter, gamma, a0, b0) |
| 3191 | 54 |
| 55 if ((nargin < 3) || (nargin == 6) || (nargin > 7)) | |
| 6046 | 56 print_usage (); |
| 3191 | 57 endif |
| 3426 | 58 |
| 4030 | 59 if (! (isvector (y))) |
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60 error ("arch_fit: Y must be a vector"); |
| 3191 | 61 endif |
| 62 | |
| 63 T = length (y); | |
| 64 y = reshape (y, T, 1); | |
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65 [rx, cx] = size (x); |
| 3191 | 66 if ((rx == 1) && (cx == 1)) |
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67 x = autoreg_matrix (y, x); |
| 3457 | 68 elseif (! (rx == T)) |
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69 error ("arch_fit: either rows (X) == length (Y), or X is a scalar"); |
| 3191 | 70 endif |
| 71 | |
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72 [T, k] = size (x); |
| 3426 | 73 |
| 3191 | 74 if (nargin == 7) |
| 75 a = a0; | |
| 76 b = b0; | |
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77 e = y - x * b; |
| 3191 | 78 else |
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79 [b, v_b, e] = ols (y, x); |
| 3273 | 80 a = [v_b, (zeros (1, p))]'; |
| 3191 | 81 if (nargin < 5) |
| 82 gamma = 0.1; | |
| 83 if (nargin < 4) | |
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84 iter = 50; |
| 3191 | 85 endif |
| 86 endif | |
| 87 endif | |
| 3426 | 88 |
| 3191 | 89 esq = e.^2; |
| 90 Z = autoreg_matrix (esq, p); | |
| 91 | |
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92 for i = 1 : iter; |
| 3191 | 93 h = Z * a; |
| 94 tmp = esq ./ h.^2 - 1 ./ h; | |
| 95 s = 1 ./ h(1:T-p); | |
| 96 for j = 1 : p; | |
| 97 s = s - a(j+1) * tmp(j+1:T-p+j); | |
| 98 endfor | |
| 99 r = 1 ./ h(1:T-p); | |
| 8507 | 100 for j = 1:p; |
| 3191 | 101 r = r + 2 * h(j+1:T-p+j).^2 .* esq(1:T-p); |
| 102 endfor | |
| 103 r = sqrt (r); | |
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104 X_tilde = x(1:T-p, :) .* (r * ones (1,k)); |
| 3191 | 105 e_tilde = e(1:T-p) .*s ./ r; |
| 106 delta_b = inv (X_tilde' * X_tilde) * X_tilde' * e_tilde; | |
| 107 b = b + gamma * delta_b; | |
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108 e = y - x * b; |
| 3191 | 109 esq = e .^ 2; |
| 110 Z = autoreg_matrix (esq, p); | |
| 111 h = Z * a; | |
| 112 f = esq ./ h - ones(T,1); | |
| 113 Z_tilde = Z ./ (h * ones (1, p+1)); | |
| 114 delta_a = inv (Z_tilde' * Z_tilde) * Z_tilde' * f; | |
| 115 a = a + gamma * delta_a; | |
| 116 endfor | |
| 3426 | 117 |
| 3191 | 118 endfunction |