Mercurial > octave-nkf
view scripts/signal/arch_fit.m @ 20266:83792dd9bcc1
Use in-place operators in m-files where possible.
* scripts/audio/@audioplayer/set.m, scripts/audio/@audiorecorder/set.m,
scripts/audio/mu2lin.m, scripts/elfun/cosd.m, scripts/general/del2.m,
scripts/general/profexplore.m, scripts/general/quadl.m, scripts/general/rat.m,
scripts/general/rotdim.m, scripts/help/get_first_help_sentence.m,
scripts/help/private/__strip_html_tags__.m, scripts/image/cubehelix.m,
scripts/io/textread.m, scripts/linear-algebra/duplication_matrix.m,
scripts/linear-algebra/housh.m, scripts/linear-algebra/krylov.m,
scripts/linear-algebra/logm.m, scripts/linear-algebra/normest.m,
scripts/linear-algebra/onenormest.m, scripts/optimization/fminsearch.m,
scripts/optimization/lsqnonneg.m, scripts/optimization/qp.m,
scripts/plot/appearance/annotation.m, scripts/plot/appearance/axis.m,
scripts/plot/appearance/legend.m, scripts/plot/appearance/specular.m,
scripts/plot/draw/colorbar.m, scripts/plot/draw/hist.m,
scripts/plot/draw/plotmatrix.m, scripts/plot/draw/private/__stem__.m,
scripts/plot/util/__actual_axis_position__.m,
scripts/plot/util/__gnuplot_drawnow__.m, scripts/plot/util/findobj.m,
scripts/plot/util/print.m, scripts/plot/util/private/__go_draw_axes__.m,
scripts/plot/util/private/__print_parse_opts__.m, scripts/plot/util/rotate.m,
scripts/polynomial/pchip.m, scripts/polynomial/polyaffine.m,
scripts/polynomial/polyder.m, scripts/polynomial/private/__splinefit__.m,
scripts/polynomial/residue.m, scripts/signal/arch_fit.m,
scripts/signal/arch_rnd.m, scripts/signal/bartlett.m,
scripts/signal/blackman.m, scripts/signal/freqz.m, scripts/signal/hamming.m,
scripts/signal/hanning.m, scripts/signal/spectral_adf.m,
scripts/signal/spectral_xdf.m, scripts/signal/stft.m,
scripts/sparse/bicgstab.m, scripts/sparse/cgs.m,
scripts/sparse/private/__sprand_impl__.m, scripts/sparse/qmr.m,
scripts/sparse/sprandsym.m, scripts/sparse/svds.m, scripts/specfun/legendre.m,
scripts/special-matrix/gallery.m, scripts/statistics/base/gls.m,
scripts/statistics/models/logistic_regression.m,
scripts/statistics/tests/kruskal_wallis_test.m,
scripts/statistics/tests/manova.m, scripts/statistics/tests/wilcoxon_test.m,
scripts/time/datevec.m:
Use in-place operators in m-files where possible.
author | Rik <rik@octave.org> |
---|---|
date | Tue, 26 May 2015 21:07:42 -0700 |
parents | f1d0f506ee78 |
children |
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## Copyright (C) 1995-2015 Kurt Hornik ## ## This file is part of Octave. ## ## Octave is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or (at ## your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## <http://www.gnu.org/licenses/>. ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{a}, @var{b}] =} arch_fit (@var{y}, @var{x}, @var{p}, @var{iter}, @var{gamma}, @var{a0}, @var{b0}) ## Fit an ARCH regression model to the time series @var{y} using the scoring ## algorithm in @nospell{Engle's} original ARCH paper. ## ## The model is ## ## @example ## @group ## y(t) = b(1) * x(t,1) + @dots{} + b(k) * x(t,k) + e(t), ## h(t) = a(1) + a(2) * e(t-1)^2 + @dots{} + a(p+1) * e(t-p)^2 ## @end group ## @end example ## ## @noindent ## in which @math{e(t)} is @math{N(0, h(t))}, given a time-series vector ## @var{y} up to time @math{t-1} and a matrix of (ordinary) regressors @var{x} ## up to @math{t}. The order of the regression of the residual variance is ## specified by @var{p}. ## ## If invoked as @code{arch_fit (@var{y}, @var{k}, @var{p})} with a positive ## integer @var{k}, fit an ARCH(@var{k}, @var{p}) process, i.e., do the above ## with the @math{t}-th row of @var{x} given by ## ## @example ## [1, y(t-1), @dots{}, y(t-k)] ## @end example ## ## Optionally, one can specify the number of iterations @var{iter}, the ## updating factor @var{gamma}, and initial values @math{a0} and @math{b0} ## for the scoring algorithm. ## @end deftypefn ## Author: KH <Kurt.Hornik@wu-wien.ac.at> ## Description: Fit an ARCH regression model function [a, b] = arch_fit (y, x, p, iter, gamma, a0, b0) if (nargin < 3 || nargin == 6 || nargin > 7) print_usage (); endif if (! (isvector (y))) error ("arch_fit: Y must be a vector"); endif T = length (y); y = reshape (y, T, 1); [rx, cx] = size (x); if ((rx == 1) && (cx == 1)) x = autoreg_matrix (y, x); elseif (! (rx == T)) error ("arch_fit: either rows (X) == length (Y), or X is a scalar"); endif [T, k] = size (x); if (nargin == 7) a = a0; b = b0; e = y - x * b; else [b, v_b, e] = ols (y, x); a = [v_b, (zeros (1, p))]'; if (nargin < 5) gamma = 0.1; if (nargin < 4) iter = 50; endif endif endif esq = e.^2; Z = autoreg_matrix (esq, p); for i = 1 : iter; h = Z * a; tmp = esq ./ h.^2 - 1 ./ h; s = 1 ./ h(1:T-p); for j = 1 : p; s -= a(j+1) * tmp(j+1:T-p+j); endfor r = 1 ./ h(1:T-p); for j = 1:p; r += 2 * h(j+1:T-p+j).^2 .* esq(1:T-p); endfor r = sqrt (r); X_tilde = x(1:T-p, :) .* (r * ones (1,k)); e_tilde = e(1:T-p) .*s ./ r; delta_b = inv (X_tilde' * X_tilde) * X_tilde' * e_tilde; b += gamma * delta_b; e = y - x * b; esq = e .^ 2; Z = autoreg_matrix (esq, p); h = Z * a; f = esq ./ h - ones (T,1); Z_tilde = Z ./ (h * ones (1, p+1)); delta_a = inv (Z_tilde' * Z_tilde) * Z_tilde' * f; a += gamma * delta_a; endfor endfunction