2 src/math/time-series/arma/innovations.c
4 Copyright (C) 2006 Free Software Foundation, Inc. Written by Jason H. Stover.
6 This program is free software; you can redistribute it and/or modify it under
7 the terms of the GNU General Public License as published by the Free
8 Software Foundation; either version 2 of the License, or (at your option)
11 This program is distributed in the hope that it will be useful, but WITHOUT
12 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
13 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
16 You should have received a copy of the GNU General Public License along with
17 this program; if not, write to the Free Software Foundation, Inc., 51
18 Franklin Street, Fifth Floor, Boston, MA 02111-1307, USA.
21 Find preliminary ARMA coefficients via the innovations algorithm.
22 Also compute the sample mean and covariance matrix for each series.
26 P. J. Brockwell and R. A. Davis. Time Series: Theory and
27 Methods. Second edition. Springer. New York. 1991. ISBN
28 0-387-97429-6. Sections 5.2, 8.3 and 8.4.
31 #include <gsl/gsl_matrix.h>
32 #include <gsl/gsl_vector.h>
35 #include <data/case.h>
36 #include <data/casefile.h>
37 #include <libpspp/alloc.h>
38 #include <libpspp/compiler.h>
39 #include <libpspp/message.h>
40 #include <math/coefficient.h>
41 #include <math/innovations.h>
43 #define _(msgid) gettext (msgid)
46 get_mean_variance (size_t n_vars, const struct casefile *cf,
47 struct innovations_estimate **est)
59 for (n = 0; n < n_vars; n++)
63 est[n]->variance = 0.0;
65 for (r = casefile_get_reader (cf); casereader_read (r, &c);
68 for (n = 0; n < n_vars; n++)
70 if (!mv_is_value_missing (&v->miss, val))
72 tmp = case_data (&c, est[n]->variable->fv);
73 d = (tmp - est[n]->mean) / est[n]->n_obs;
75 est[n]->variance += est[n]->n_obs * est[n]->n_obs * d * d;
80 for (n = 0; n < n_vars; n++)
82 /* Maximum likelihood estimate of the variance. */
83 est[n]->variance /= est[n]->n_obs;
88 Read the first MAX_LAG cases.
91 innovations_init_cases (struct casereader *r, struct ccase **c, size_t max_lag)
99 value = casereader_read (r, c + lag);
105 Read one case and update C, which contains the last MAX_LAG cases.
108 innovations_update_cases (struct casereader *r, struct ccase **c, size_t max_lag)
113 for (lag = 0; lag < max_lag - 1; lag++)
117 value = casereader_read (r, c + lag);
121 get_covariance (size_t n_vars, const struct casefile *cf,
122 struct innovations **est, size_t max_lag)
124 struct casereader *r;
126 struct ccase *cur_case;
129 bool read_case = false;
133 c = xnmalloc (max_lag, sizeof (*c));
135 for (lag = 0; lag < max_lag; lag++)
137 c[lag] = xmalloc (sizeof *c[i]);
140 r = casefile_get_reader (cf);
141 read_case = innovations_init_cases (r, c, max_lag);
145 for (n = 0; n < n_vars; n++)
147 cur_case = case_data (c[0], est[n]->variable->fv);
148 if (!mv_is_value_missing (&est[n]->variable->miss, cur_case))
150 cur_case -= est[n]->mean;
151 for (lag = 1; lag <= max_lag; lag++)
153 tmp = case_data (c[lag], est[n]->variable->fv);
154 if (!mv_is_value_missing (&est[n]->variable->miss, tmp))
156 d = (tmp - est[n]->mean);
157 *(est[n]->cov + lag) += d * cur_case;
162 read_case = innovations_update_cases (r, c, max_lag);
164 for (lag = 0; lag <= max_lag; lag++)
166 for (n = 0; n < n_vars; n++)
168 *(est[n]->cov + lag) /= (est[n]->n_obs - lag);
171 for (lag = 0; lag < max_lag; lag++)
178 struct innovations_estimate ** pspp_innovations (const struct variable **vars, size_t *n_vars,
179 size_t lag, const struct casefile *cf)
181 struct innovations_estimate **est;
182 struct casereader *r;
186 est = xnmalloc (*n_vars, sizeof *est);
187 for (i = 0; i < *n_vars; i++)
189 if (vars[i]->type == NUMERIC)
191 est[i] = xmalloc (sizeof **est);
192 est[i]->variable = vars[i];
194 est[i]->variance = 0.0;
195 est[i]->cov = xnmalloc (lag, sizeof (est[i]->cov));
196 est[i]->coeff = xnmalloc (lag, sizeof (*est[i]->coeff));
197 for (j = 0; j < lag; j++)
199 est[i]->coeff + j = xmalloc (sizeof (*(est[i]->coeff + j)));
205 msg (MW, _("Cannot compute autocovariance for a non-numeric variable %s"),
206 var_to_string (vars[i]));
211 First data pass to get the mean and variance.
213 get_mean_variance (*n_vars, cf, est);
214 get_covariance (*n_vars, cf, est, lag);