Mercurial > octave
view scripts/signal/arch_fit.m @ 3426:f8dde1807dee
[project @ 2000-01-13 08:40:00 by jwe]
author | jwe |
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date | Thu, 13 Jan 2000 08:40:53 +0000 |
parents | eb27ea9b7ff8 |
children | 858695b3ed62 |
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## Copyright (C) 1995, 1996, 1997 Kurt Hornik ## ## This program 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 2, or (at your option) ## any later version. ## ## This program 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 this file. If not, write to the Free Software Foundation, ## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. ## usage: [a, b] = arch_fit (y, X, p [, ITER [, gamma [, a0, b0]]]) ## ## Fits an ARCH regression model to the time series y using the scoring ## algorithm in Engle's original ARCH paper. The model is ## y(t) = b(1) * x(t,1) + ... + b(k) * x(t,k) + e(t), ## h(t) = a(1) + a(2) * e(t-1)^2 + ... + a(p+1) * e(t-p)^2, ## where e(t) is N(0, h(t)), given y up to time t-1 and X up to t. ## ## If invoked as arch_fit (y, k, p) with a positive integer k, fit an ## ARCH(k,p) process, i.e., do the above with the t-th row of X given by ## [1, y(t-1), ..., y(t-k)]. ## ## Optionally, one can specify the number of iterations ITER, the ## updating factor gamma, and initial values a0 and b0 for the scoring ## algorithm. ## ## The input parameters are: ## y ... time series (vector) ## X ... matrix of (ordinary) regressors or order of ## autoregression ## p ... order of the regression of the residual variance ## Author: KH <Kurt.Hornik@ci.tuwien.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)) usage ("arch_fit (y, X, p [, ITER [, gamma [, a0, b0]]])"); endif if !(is_vector (y)) error ("arch_test: 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_test: ", ... "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 = s - a(j+1) * tmp(j+1:T-p+j); endfor r = 1 ./ h(1:T-p); for j=1:p; r = 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 = 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 = a + gamma * delta_a; endfor endfunction