octave-nkf: scripts/signal/arch

annotate scripts/signal/arch_fit.m @ 20387:4951982f8a2c stable

intro.txi: Improve documentation in introductory chapter. * intro.txi: Use 'diary' instead of 'cd' as an example of a command. Format sample function docstring to match modern usage. Improve phrasing of a few sentences.

author	Rik <rik@octave.org>
date	Mon, 11 May 2015 22:08:26 -0700
parents	f1d0f506ee78
children	83792dd9bcc1

rev	line source
19898 4197fc428c7d maint: Update copyright notices for 2015. John W. Eaton <jwe@octave.org> parents: 19232 diff changeset	1 ## Copyright (C) 1995-2015 Kurt Hornik
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3273 diff changeset	2 ##
3922 38c61cbf086c [project @ 2002-05-01 06:48:35 by jwe] jwe parents: 3499 diff changeset	3 ## This file is part of Octave.
38c61cbf086c [project @ 2002-05-01 06:48:35 by jwe] jwe parents: 3499 diff changeset	4 ##
38c61cbf086c [project @ 2002-05-01 06:48:35 by jwe] jwe parents: 3499 diff changeset	5 ## Octave is free software; you can redistribute it and/or modify it
38c61cbf086c [project @ 2002-05-01 06:48:35 by jwe] jwe parents: 3499 diff changeset	6 ## under the terms of the GNU General Public License as published by
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6046 diff changeset	7 ## the Free Software Foundation; either version 3 of the License, or (at
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6046 diff changeset	8 ## your option) any later version.
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3273 diff changeset	9 ##
3922 38c61cbf086c [project @ 2002-05-01 06:48:35 by jwe] jwe parents: 3499 diff changeset	10 ## Octave is distributed in the hope that it will be useful, but
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3273 diff changeset	13 ## General Public License for more details.
f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3273 diff changeset	14 ##
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	15 ## You should have received a copy of the GNU General Public License
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6046 diff changeset	16 ## along with Octave; see the file COPYING. If not, see
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6046 diff changeset	17 ## <http://www.gnu.org/licenses/>.
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	18
3449 858695b3ed62 [project @ 2000-01-18 04:08:59 by jwe] jwe parents: 3426 diff changeset	19 ## -- texinfo --
858695b3ed62 [project @ 2000-01-18 04:08:59 by jwe] jwe parents: 3426 diff changeset	20 ## @deftypefn {Function File} {[@var{a}, @var{b}] =} arch_fit (@var{y}, @var{x}, @var{p}, @var{iter}, @var{gamma}, @var{a0}, @var{b0})
20375 f1d0f506ee78 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 20038 diff changeset	21 ## Fit an ARCH regression model to the time series @var{y} using the scoring
f1d0f506ee78 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 20038 diff changeset	22 ## algorithm in @nospell{Engle's} original ARCH paper.
f1d0f506ee78 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 20038 diff changeset	23 ##
f1d0f506ee78 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 20038 diff changeset	24 ## The model is
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	25 ##
3449 858695b3ed62 [project @ 2000-01-18 04:08:59 by jwe] jwe parents: 3426 diff changeset	26 ## @example
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	27 ## @group
1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	28 ## y(t) = b(1) * x(t,1) + @dots{} + b(k) * x(t,k) + e(t),
1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	29 ## h(t) = a(1) + a(2) * e(t-1)^2 + @dots{} + a(p+1) * e(t-p)^2
1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	30 ## @end group
3449 858695b3ed62 [project @ 2000-01-18 04:08:59 by jwe] jwe parents: 3426 diff changeset	31 ## @end example
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	32 ##
3449 858695b3ed62 [project @ 2000-01-18 04:08:59 by jwe] jwe parents: 3426 diff changeset	33 ## @noindent
3499 3e3e14ad5149 [project @ 2000-01-31 05:18:07 by jwe] jwe parents: 3457 diff changeset	34 ## in which @math{e(t)} is @math{N(0, h(t))}, given a time-series vector
20375 f1d0f506ee78 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 20038 diff changeset	35 ## @var{y} up to time @math{t-1} and a matrix of (ordinary) regressors @var{x}
f1d0f506ee78 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 20038 diff changeset	36 ## up to @math{t}. The order of the regression of the residual variance is
f1d0f506ee78 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 20038 diff changeset	37 ## specified by @var{p}.
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	38 ##
20375 f1d0f506ee78 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 20038 diff changeset	39 ## If invoked as @code{arch_fit (@var{y}, @var{k}, @var{p})} with a positive
f1d0f506ee78 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 20038 diff changeset	40 ## integer @var{k}, fit an ARCH(@var{k}, @var{p}) process, i.e., do the above
f1d0f506ee78 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 20038 diff changeset	41 ## with the @math{t}-th row of @var{x} given by
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	42 ##
3449 858695b3ed62 [project @ 2000-01-18 04:08:59 by jwe] jwe parents: 3426 diff changeset	43 ## @example
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	44 ## [1, y(t-1), @dots{}, y(t-k)]
3449 858695b3ed62 [project @ 2000-01-18 04:08:59 by jwe] jwe parents: 3426 diff changeset	45 ## @end example
858695b3ed62 [project @ 2000-01-18 04:08:59 by jwe] jwe parents: 3426 diff changeset	46 ##
858695b3ed62 [project @ 2000-01-18 04:08:59 by jwe] jwe parents: 3426 diff changeset	47 ## Optionally, one can specify the number of iterations @var{iter}, the
20375 f1d0f506ee78 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 20038 diff changeset	48 ## updating factor @var{gamma}, and initial values @math{a0} and @math{b0}
f1d0f506ee78 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 20038 diff changeset	49 ## for the scoring algorithm.
3449 858695b3ed62 [project @ 2000-01-18 04:08:59 by jwe] jwe parents: 3426 diff changeset	50 ## @end deftypefn
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	51
5428 2a16423e4aa0 [project @ 2005-08-23 18:38:27 by jwe] jwe parents: 5307 diff changeset	52 ## Author: KH <Kurt.Hornik@wu-wien.ac.at>
3457 e031284eea27 [project @ 2000-01-19 08:49:56 by jwe] jwe parents: 3449 diff changeset	53 ## Description: Fit an ARCH regression model
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	54
11469 c776f063fefe Overhaul m-script files to use common variable name between code and documentation. Rik <octave@nomad.inbox5.com> parents: 10635 diff changeset	55 function [a, b] = arch_fit (y, x, p, iter, gamma, a0, b0)
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	56
20038 9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions. Rik <rik@octave.org> parents: 19898 diff changeset	57 if (nargin < 3 \|\| nargin == 6 \|\| nargin > 7)
6046 34f96dd5441b [project @ 2006-10-10 16:10:25 by jwe] jwe parents: 5428 diff changeset	58 print_usage ();
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	59 endif
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3273 diff changeset	60
4030 22bd65326ec1 [project @ 2002-08-09 18:58:13 by jwe] jwe parents: 3922 diff changeset	61 if (! (isvector (y)))
11472 1740012184f9 Use uppercase for variable names in error() strings to match Info documentation. Only m-files done. Rik <octave@nomad.inbox5.com> parents: 11469 diff changeset	62 error ("arch_fit: Y must be a vector");
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	63 endif
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	64
20038 9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions. Rik <rik@octave.org> parents: 19898 diff changeset	65 T = length (y);
9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions. Rik <rik@octave.org> parents: 19898 diff changeset	66 y = reshape (y, T, 1);
11469 c776f063fefe Overhaul m-script files to use common variable name between code and documentation. Rik <octave@nomad.inbox5.com> parents: 10635 diff changeset	67 [rx, cx] = size (x);
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	68 if ((rx == 1) && (cx == 1))
11469 c776f063fefe Overhaul m-script files to use common variable name between code and documentation. Rik <octave@nomad.inbox5.com> parents: 10635 diff changeset	69 x = autoreg_matrix (y, x);
3457 e031284eea27 [project @ 2000-01-19 08:49:56 by jwe] jwe parents: 3449 diff changeset	70 elseif (! (rx == T))
11472 1740012184f9 Use uppercase for variable names in error() strings to match Info documentation. Only m-files done. Rik <octave@nomad.inbox5.com> parents: 11469 diff changeset	71 error ("arch_fit: either rows (X) == length (Y), or X is a scalar");
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	72 endif
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	73
11469 c776f063fefe Overhaul m-script files to use common variable name between code and documentation. Rik <octave@nomad.inbox5.com> parents: 10635 diff changeset	74 [T, k] = size (x);
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3273 diff changeset	75
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	76 if (nargin == 7)
20038 9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions. Rik <rik@octave.org> parents: 19898 diff changeset	77 a = a0;
9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions. Rik <rik@octave.org> parents: 19898 diff changeset	78 b = b0;
9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions. Rik <rik@octave.org> parents: 19898 diff changeset	79 e = y - x * b;
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	80 else
11469 c776f063fefe Overhaul m-script files to use common variable name between code and documentation. Rik <octave@nomad.inbox5.com> parents: 10635 diff changeset	81 [b, v_b, e] = ols (y, x);
20038 9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions. Rik <rik@octave.org> parents: 19898 diff changeset	82 a = [v_b, (zeros (1, p))]';
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	83 if (nargin < 5)
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	84 gamma = 0.1;
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	85 if (nargin < 4)
11469 c776f063fefe Overhaul m-script files to use common variable name between code and documentation. Rik <octave@nomad.inbox5.com> parents: 10635 diff changeset	86 iter = 50;
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	87 endif
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	88 endif
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	89 endif
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3273 diff changeset	90
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	91 esq = e.^2;
20038 9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions. Rik <rik@octave.org> parents: 19898 diff changeset	92 Z = autoreg_matrix (esq, p);
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	93
11469 c776f063fefe Overhaul m-script files to use common variable name between code and documentation. Rik <octave@nomad.inbox5.com> parents: 10635 diff changeset	94 for i = 1 : iter;
20038 9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions. Rik <rik@octave.org> parents: 19898 diff changeset	95 h = Z * a;
9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions. Rik <rik@octave.org> parents: 19898 diff changeset	96 tmp = esq ./ h.^2 - 1 ./ h;
9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions. Rik <rik@octave.org> parents: 19898 diff changeset	97 s = 1 ./ h(1:T-p);
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	98 for j = 1 : p;
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	99 s = s - a(j+1) * tmp(j+1:T-p+j);
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	100 endfor
20038 9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions. Rik <rik@octave.org> parents: 19898 diff changeset	101 r = 1 ./ h(1:T-p);
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 7017 diff changeset	102 for j = 1:p;
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	103 r = r + 2 * h(j+1:T-p+j).^2 .* esq(1:T-p);
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	104 endfor
20038 9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions. Rik <rik@octave.org> parents: 19898 diff changeset	105 r = sqrt (r);
11469 c776f063fefe Overhaul m-script files to use common variable name between code and documentation. Rik <octave@nomad.inbox5.com> parents: 10635 diff changeset	106 X_tilde = x(1:T-p, :) .* (r * ones (1,k));
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	107 e_tilde = e(1:T-p) .*s ./ r;
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	108 delta_b = inv (X_tilde' * X_tilde) * X_tilde' * e_tilde;
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	109 b = b + gamma * delta_b;
11469 c776f063fefe Overhaul m-script files to use common variable name between code and documentation. Rik <octave@nomad.inbox5.com> parents: 10635 diff changeset	110 e = y - x * b;
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	111 esq = e .^ 2;
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	112 Z = autoreg_matrix (esq, p);
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	113 h = Z * a;
14868 5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	114 f = esq ./ h - ones (T,1);
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	115 Z_tilde = Z ./ (h * ones (1, p+1));
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	116 delta_a = inv (Z_tilde' * Z_tilde) * Z_tilde' * f;
20038 9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions. Rik <rik@octave.org> parents: 19898 diff changeset	117 a = a + gamma * delta_a;
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	118 endfor
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3273 diff changeset	119
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	120 endfunction
17338 1c89599167a6 maint: End m-files with 1 blank line. Rik <rik@octave.org> parents: 14868 diff changeset	121

Mercurial > hg > octave-nkf

annotate scripts/signal/arch_fit.m @ 20387:4951982f8a2c stable