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>
42 #define _(msgid) gettext (msgid)
45 get_mean_variance (size_t n_vars, const struct casefile *cf,
46 struct innovations_estimate **est)
58 for (n = 0; n < n_vars; n++)
62 est[n]->variance = 0.0;
64 for (r = casefile_get_reader (cf); casereader_read (r, &c);
67 for (n = 0; n < n_vars; n++)
69 if (!mv_is_value_missing (&v->miss, val))
71 tmp = case_data (&c, est[n]->variable->fv);
72 d = (tmp - est[n]->mean) / est[n]->n_obs;
74 est[n]->variance += est[n]->n_obs * est[n]->n_obs * d * d;
79 for (n = 0; n < n_vars; n++)
81 /* Maximum likelihood estimate of the variance. */
82 est[n]->variance /= est[n]->n_obs;
87 Read the first MAX_LAG cases.
90 innovations_init_cases (struct casereader *r, struct ccase **c, size_t max_lag)
98 value = casereader_read (r, c + lag);
104 Read one case and update C, which contains the last MAX_LAG cases.
107 innovations_update_cases (struct casereader *r, struct ccase **c, size_t max_lag)
112 for (lag = 0; lag < max_lag - 1; lag++)
116 value = casereader_read (r, c + lag);
120 get_covariance (size_t n_vars, const struct casefile *cf,
121 struct innovations **est, size_t max_lag)
123 struct casereader *r;
125 struct ccase *cur_case;
128 bool read_case = false;
132 c = xnmalloc (max_lag, sizeof (*c));
134 for (lag = 0; lag < max_lag; lag++)
136 c[lag] = xmalloc (sizeof *c[i]);
139 r = casefile_get_reader (cf);
140 read_case = innovations_init_cases (r, c, max_lag);
144 for (n = 0; n < n_vars; n++)
146 cur_case = case_data (c[0], est[n]->variable->fv);
147 if (!mv_is_value_missing (&est[n]->variable->miss, cur_case))
149 cur_case -= est[n]->mean;
150 for (lag = 1; lag <= max_lag; lag++)
152 tmp = case_data (c[lag], est[n]->variable->fv);
153 if (!mv_is_value_missing (&est[n]->variable->miss, tmp))
155 d = (tmp - est[n]->mean);
156 *(est[n]->cov + lag) += d * cur_case;
161 read_case = innovations_update_cases (r, c, max_lag);
163 for (lag = 0; lag <= max_lag; lag++)
165 for (n = 0; n < n_vars; n++)
167 *(est[n]->cov + lag) /= (est[n]->n_obs - lag);
170 for (lag = 0; lag < max_lag; lag++)
177 struct innovations_estimate ** pspp_innovations (const struct variable **vars, size_t *n_vars,
178 size_t lag, const struct casefile *cf)
180 struct innovations_estimate **est;
181 struct casereader *r;
185 est = xnmalloc (*n_vars, sizeof *est);
186 for (i = 0; i < *n_vars; i++)
188 if (vars[i]->type == NUMERIC)
190 est[i] = xmalloc (sizeof **est);
191 est[i]->variable = vars[i];
193 est[i]->variance = 0.0;
194 est[i]->cov = gsl_matrix_calloc (lag, lag);
195 est[i]->coeff = xnmalloc (lag, sizeof (*est[i]->coeff));
196 for (j = 0; j < lag; j++)
198 est[i]->coeff + j = xmalloc (sizeof (*(est[i]->coeff + j)));
204 msg (MW, _("Cannot compute autocovariance for a non-numeric variable %s"),
205 var_to_string (vars[i]));
210 First data pass to get the mean and variance.
212 get_mean_variance (*n_vars, cf, est);
213 get_covariance (*n_vars, cf, est, lag);