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/ts/innovations.h>
44 get_mean_variance (size_t n_vars, const struct casefile *cf,
45 struct innovations_estimate **est)
52 const union value *tmp;
54 for (n = 0; n < n_vars; n++)
58 est[n]->variance = 0.0;
60 for (r = casefile_get_reader (cf); casereader_read (r, &c);
63 for (n = 0; n < n_vars; n++)
65 tmp = case_data (&c, est[n]->variable->fv);
66 if (!mv_is_value_missing (&(est[n]->variable->miss), tmp))
68 d = (tmp->f - est[n]->mean) / est[n]->n_obs;
70 est[n]->variance += est[n]->n_obs * est[n]->n_obs * d * d;
75 for (n = 0; n < n_vars; n++)
77 /* Maximum likelihood estimate of the variance. */
78 est[n]->variance /= est[n]->n_obs;
83 Read the first MAX_LAG cases.
86 innovations_init_cases (struct casereader *r, struct ccase **c, size_t max_lag)
94 value = casereader_read (r, c + lag);
100 Read one case and update C, which contains the last MAX_LAG cases.
103 innovations_update_cases (struct casereader *r, struct ccase **c, size_t max_lag)
108 for (lag = 0; lag < max_lag - 1; lag++)
112 value = casereader_read (r, c + lag);
116 get_covariance (size_t n_vars, const struct casefile *cf,
117 struct innovations **est, size_t max_lag)
119 struct casereader *r;
121 struct ccase *cur_case;
124 bool read_case = false;
128 c = xnmalloc (max_lag, sizeof (*c));
130 for (lag = 0; lag < max_lag; lag++)
132 c[lag] = xmalloc (sizeof *c[i]);
135 r = casefile_get_reader (cf);
136 read_case = innovations_init_cases (r, c, max_lag);
140 for (n = 0; n < n_vars; n++)
142 cur_case = case_data (c[0], est[n]->variable->fv);
143 if (!mv_is_value_missing (&est[n]->variable->miss, cur_case))
145 cur_case -= est[n]->mean;
146 for (lag = 1; lag <= max_lag; lag++)
148 tmp = case_data (c[lag], est[n]->variable->fv);
149 if (!mv_is_value_missing (&est[n]->variable->miss, tmp))
151 d = (tmp - est[n]->mean);
152 *(est[n]->cov + lag) += d * cur_case;
157 read_case = innovations_update_cases (r, c, max_lag);
159 for (lag = 0; lag <= max_lag; lag++)
161 for (n = 0; n < n_vars; n++)
163 *(est[n]->cov + lag) /= (est[n]->n_obs - lag);
166 for (lag = 0; lag < max_lag; lag++)
173 struct innovations_estimate ** pspp_innovations (const struct variable **vars, size_t *n_vars,
174 size_t lag, const struct casefile *cf)
176 struct innovations_estimate **est;
177 struct casereader *r;
182 est = xnmalloc (*n_vars, sizeof *est);
183 for (i = 0; i < *n_vars; i++)
185 if (vars[i]->type == NUMERIC)
187 est[i] = xmalloc (sizeof **est);
188 est[i]->variable = vars[i];
190 est[i]->variance = 0.0;
191 est[i]->cov = xnmalloc (lag, sizeof (est[i]->cov));
192 est[i]->coeff = xnmalloc (lag, sizeof (*est[i]->coeff));
193 for (j = 0; j < lag; j++)
195 est[i]->coeff + j = xmalloc (sizeof (*(est[i]->coeff + j)));
201 /* msg (MW, _("Cannot compute autocovariance for a non-numeric variable %s"), */
202 /* var_to_string (vars[i])); */
207 First data pass to get the mean and variance.
209 get_mean_variance (*n_vars, cf, est);
210 get_covariance (*n_vars, cf, est, lag);