+/*
+ src/math/time-series/arma/innovations.c
+
+ Copyright (C) 2006 Free Software Foundation, Inc. Written by Jason H. Stover.
+
+ 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 of the License, 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 program; if not, write to the Free Software Foundation, Inc., 51
+ Franklin Street, Fifth Floor, Boston, MA 02111-1307, USA.
+ */
+/*
+ Find preliminary ARMA coefficients via the innovations algorithm.
+ Also compute the sample mean and covariance matrix for each series.
+
+ Reference:
+
+ P. J. Brockwell and R. A. Davis. Time Series: Theory and
+ Methods. Second edition. Springer. New York. 1991. ISBN
+ 0-387-97429-6. Sections 5.2, 8.3 and 8.4.
+ */
+
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_vector.h>
+#include <math.h>
+#include <stdlib.h>
+#include <data/case.h>
+#include <data/casefile.h>
+#include <libpspp/alloc.h>
+#include <libpspp/compiler.h>
+#include <libpspp/message.h>
+#include <math/coefficient.h>
+#include <math/innovations.h>
+#include <gettext.h>
+#define _(msgid) gettext (msgid)
+
+static void
+get_mean_variance (size_t n_vars, const struct casefile *cf,
+ struct innovations_estimate **est)
+
+{
+ struct casereader *r;
+ struct ccase *c;
+ struct ccase *c2;
+ size_t n;
+ double *x;
+ double d;
+ double tmp;
+ double variance;
+
+ for (n = 0; n < n_vars; n++)
+ {
+ est[n]->n_obs = 2.0;
+ est[n]->mean = 0.0;
+ est[n]->variance = 0.0;
+ }
+ for (r = casefile_get_reader (cf); casereader_read (r, &c);
+ case_destroy (&c))
+ {
+ for (n = 0; n < n_vars; n++)
+ {
+ if (!mv_is_value_missing (&v->miss, val))
+ {
+ tmp = case_data (&c, est[n]->variable->fv);
+ d = (tmp - est[n]->mean) / est[n]->n_obs;
+ est[n]->mean += d;
+ est[n]->variance += est[n]->n_obs * est[n]->n_obs * d * d;
+ est[n]->n_obs += 1.0;
+ }
+ }
+ }
+ for (n = 0; n < n_vars; n++)
+ {
+ /* Maximum likelihood estimate of the variance. */
+ est[n]->variance /= est[n]->n_obs;
+ }
+}
+
+/*
+ Read the first MAX_LAG cases.
+ */
+static bool
+innovations_init_cases (struct casereader *r, struct ccase **c, size_t max_lag)
+{
+ bool value = true;
+ size_t lag = 0;
+
+ while (value)
+ {
+ lag++;
+ value = casereader_read (r, c + lag);
+ }
+ return value;
+}
+
+/*
+ Read one case and update C, which contains the last MAX_LAG cases.
+ */
+static bool
+innovations_update_cases (struct casereader *r, struct ccase **c, size_t max_lag)
+{
+ size_t lag;
+ bool value = false;
+
+ for (lag = 0; lag < max_lag - 1; lag++)
+ {
+ c[lag] = c[lag+1];
+ }
+ value = casereader_read (r, c + lag);
+ return value;
+}
+static void
+get_covariance (size_t n_vars, const struct casefile *cf,
+ struct innovations **est, size_t max_lag)
+{
+ struct casereader *r;
+ struct ccase **c;
+ struct ccase *cur_case;
+ size_t lag;
+ size_t n_vars;
+ bool read_case = false;
+ double d;
+ double tmp;
+
+ c = xnmalloc (max_lag, sizeof (*c));
+
+ for (lag = 0; lag < max_lag; lag++)
+ {
+ c[lag] = xmalloc (sizeof *c[i]);
+ }
+
+ r = casefile_get_reader (cf);
+ read_case = innovations_init_cases (r, c, max_lag);
+
+ while (read_case)
+ {
+ for (n = 0; n < n_vars; n++)
+ {
+ cur_case = case_data (c[0], est[n]->variable->fv);
+ if (!mv_is_value_missing (&est[n]->variable->miss, cur_case))
+ {
+ cur_case -= est[n]->mean;
+ for (lag = 1; lag <= max_lag; lag++)
+ {
+ tmp = case_data (c[lag], est[n]->variable->fv);
+ if (!mv_is_value_missing (&est[n]->variable->miss, tmp))
+ {
+ d = (tmp - est[n]->mean);
+ *(est[n]->cov + lag) += d * cur_case;
+ }
+ }
+ }
+ }
+ read_case = innovations_update_cases (r, c, max_lag);
+ }
+ for (lag = 0; lag <= max_lag; lag++)
+ {
+ for (n = 0; n < n_vars; n++)
+ {
+ *(est[n]->cov + lag) /= (est[n]->n_obs - lag);
+ }
+ }
+ for (lag = 0; lag < max_lag; lag++)
+ {
+ free (c[lag]);
+ }
+ free (c);
+}
+
+struct innovations_estimate ** pspp_innovations (const struct variable **vars, size_t *n_vars,
+ size_t lag, const struct casefile *cf)
+{
+ struct innovations_estimate **est;
+ struct casereader *r;
+ struct ccase *c;
+ size_t i;
+
+ est = xnmalloc (*n_vars, sizeof *est);
+ for (i = 0; i < *n_vars; i++)
+ {
+ if (vars[i]->type == NUMERIC)
+ {
+ est[i] = xmalloc (sizeof **est);
+ est[i]->variable = vars[i];
+ est[i]->mean = 0.0;
+ est[i]->variance = 0.0;
+ est[i]->cov = xnmalloc (lag, sizeof (est[i]->cov));
+ est[i]->coeff = xnmalloc (lag, sizeof (*est[i]->coeff));
+ for (j = 0; j < lag; j++)
+ {
+ est[i]->coeff + j = xmalloc (sizeof (*(est[i]->coeff + j)));
+ }
+ }
+ else
+ {
+ *n_vars--;
+ msg (MW, _("Cannot compute autocovariance for a non-numeric variable %s"),
+ var_to_string (vars[i]));
+ }
+ }
+
+ /*
+ First data pass to get the mean and variance.
+ */
+ get_mean_variance (*n_vars, cf, est);
+ get_covariance (*n_vars, cf, est, lag);
+}