/*
- src/math/time-series/arma/innovations.c
+ src/math/ts/innovations.c
Copyright (C) 2006 Free Software Foundation, Inc. Written by Jason H. Stover.
#include <gsl/gsl_matrix.h>
#include <gsl/gsl_vector.h>
-#include <math.h>
+#include <gsl/gsl_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/ts/innovations.h>
static void
-get_mean_variance (size_t n_vars, const struct casefile *cf,
+get_mean_variance (const gsl_matrix *data,
struct innovations_estimate **est)
{
- struct casereader *r;
- struct ccase c;
size_t n;
+ size_t i;
double d;
- const union value *tmp;
+ double tmp;
- for (n = 0; n < n_vars; n++)
+ for (n = 0; n < data->size2; 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 (i = 0; i < data->size1; i++)
{
- for (n = 0; n < n_vars; n++)
+ for (n = 0; n < data->size2; n++)
{
- tmp = case_data (&c, est[n]->variable->fv);
- if (!mv_is_value_missing (&(est[n]->variable->miss), tmp))
+ tmp = gsl_matrix_get (data, i, n);
+ if (!gsl_isnan (tmp))
{
- d = (tmp->f - est[n]->mean) / est[n]->n_obs;
+ 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++)
+ for (n = 0; n < data->size2; 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)
+static int
+get_covariance (const gsl_matrix *data,
+ struct innovations_estimate **est, size_t max_lag)
{
- bool value = true;
- size_t lag = 0;
+ size_t lag;
+ size_t j;
+ size_t i;
+ double x;
+ double y;
+ int rc = 1;
- while (value)
+ assert (data != NULL);
+ assert (est != NULL);
+
+ for (i = 0; i < data->size1; i++)
{
- lag++;
- value = casereader_read (r, c + lag);
+ for (j = 0; j < data->size2; j++)
+ {
+ x = gsl_matrix_get (data, i, j);
+
+ if (!gsl_isnan (x))
+ {
+ x -= est[j]->mean;
+ for (lag = 1; lag <= max_lag && lag < (data->size1 - i); lag++)
+ {
+ y = gsl_matrix_get (data, i + lag, j);
+ if (!gsl_isnan (y))
+ {
+ y -= est[j]->mean;
+ *(est[j]->cov + lag - 1) += y * x;
+ est[j]->n_obs += 1.0;
+ }
+ }
+ }
+ }
+ }
+ for (lag = 1; lag <= max_lag; lag++)
+ {
+ for (j = 0; j < data->size2; j++)
+ {
+ *(est[j]->cov + lag) /= (est[j]->n_obs - lag);
+ }
}
- return value;
+ return rc;
}
-
-/*
- 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)
+static double
+innovations_convolve (double **theta, struct innovations_estimate *est,
+ int i, int j)
{
- size_t lag;
- bool value = false;
-
- for (lag = 0; lag < max_lag - 1; lag++)
+ int k;
+ double result = 0.0;
+
+ for (k = 0; k < j; k++)
{
- c[lag] = c[lag+1];
+ result += theta[i-1][i-k-1] * theta[j][j-k-1] * est->scale[k];
}
- value = casereader_read (r, c + lag);
- return value;
+ return result;
}
static void
-get_covariance (size_t n_vars, const struct casefile *cf,
- struct innovations **est, size_t max_lag)
+innovations_update_scale (struct innovations_estimate *est, double *theta,
+ size_t i)
{
- 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;
+ double result = 0.0;
+ size_t j;
+ size_t k;
- c = xnmalloc (max_lag, sizeof (*c));
-
- for (lag = 0; lag < max_lag; lag++)
+
+ result = est->variance;
+ for (j = 0; j < i; j++)
{
- c[lag] = xmalloc (sizeof *c[i]);
+ k = i - j - 1;
+ result -= theta[k] * theta[k] * est->scale[j];
}
+ est->scale[i] = result;
+}
+static void
+init_theta (double **theta, size_t max_lag)
+{
+ size_t i;
+ size_t j;
- r = casefile_get_reader (cf);
- read_case = innovations_init_cases (r, c, max_lag);
+ for (i = 0; i < max_lag; i++)
+ {
+ for (j = 0; j <= i; j++)
+ {
+ theta[i][j] = 0.0;
+ }
+ }
+}
+static void
+innovations_update_coeff (double **theta, struct innovations_estimate *est,
+ size_t max_lag)
+{
+ size_t i;
+ size_t j;
+ size_t k;
+ double v;
- while (read_case)
+ for (i = 0; i < max_lag; i++)
{
- for (n = 0; n < n_vars; n++)
+ for (j = 0; j <= i; j++)
{
- 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;
- }
- }
- }
+ k = i - j;
+ theta[i][k] = (est->cov[k] -
+ innovations_convolve (theta, est, i, j))
+ / est->scale[k];
}
- read_case = innovations_update_cases (r, c, max_lag);
+ innovations_update_scale (est, theta[i], i + 1);
+ }
+}
+static void
+get_coef (const gsl_matrix *data,
+ struct innovations_estimate **est, size_t max_lag)
+{
+ size_t i;
+ size_t n;
+ double **theta;
+
+ theta = xnmalloc (max_lag, sizeof (*theta));
+ for (i = 0; i < max_lag; i++)
+ {
+ theta[i] = xnmalloc (i + 1, sizeof (**(theta + i)));
}
- for (lag = 0; lag <= max_lag; lag++)
+
+ for (n = 0; n < data->size2; n++)
{
- for (n = 0; n < n_vars; n++)
+ init_theta (theta, max_lag);
+ innovations_update_scale (est[n], theta[0], 0);
+ innovations_update_coeff (theta, est[n], max_lag);
+ /* Copy the final row of coefficients into EST->COEFF.*/
+ for (i = 0; i < max_lag; i++)
{
- *(est[n]->cov + lag) /= (est[n]->n_obs - lag);
+ /*
+ The order of storage here means that the best predicted value
+ for the time series is computed as follows:
+
+ Let X[m], X[m-1],... denote the original series.
+ Let X_hat[0] denote the best predicted value of X[0],
+ X_hat[1] denote the projection of X[1] onto the subspace
+ spanned by {X[0] - X_hat[0]}. Let X_hat[m] denote the
+ projection of X[m] onto the subspace spanned by {X[m-1] - X_hat[m-1],
+ X[m-2] - X_hat[m-2],...,X[0] - X_hat[0]}.
+
+ Then X_hat[m] = est->coeff[m-1] * (X[m-1] - X_hat[m-1])
+ + est->coeff[m-1] * (X[m-2] - X_hat[m-2])
+ ...
+ + est->coeff[m-max_lag] * (X[m - max_lag] - X_hat[m - max_lag])
+
+ (That is what X_hat[m] SHOULD be, anyway. These routines need
+ to be tested.)
+ */
+ pspp_coeff_set_estimate (est[n]->coeff[i], theta[max_lag - 1][i]);
}
}
- for (lag = 0; lag < max_lag; lag++)
+
+ for (i = 0; i < max_lag; i++)
{
- free (c[lag]);
+ free (theta[i]);
}
- free (c);
+ free (theta);
}
-struct innovations_estimate ** pspp_innovations (const struct variable **vars, size_t *n_vars,
- size_t lag, const struct casefile *cf)
+struct innovations_estimate **
+pspp_innovations (const gsl_matrix *data, size_t lag)
{
struct innovations_estimate **est;
- struct casereader *r;
- struct ccase *c;
size_t i;
size_t j;
- est = xnmalloc (*n_vars, sizeof *est);
- for (i = 0; i < *n_vars; i++)
+ est = xnmalloc (data->size2, sizeof *est);
+ for (i = 0; i < data->size2; 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
+ est[i] = xmalloc (sizeof *est[i]);
+/* est[i]->variable = vars[i]; */
+ est[i]->mean = 0.0;
+ est[i]->variance = 0.0;
+ /* COV does not the variance (i.e., the lag 0 covariance). So COV[0]
+ holds the lag 1 covariance, COV[i] holds the lag i+1 covariance. */
+ est[i]->cov = xnmalloc (lag, sizeof (*est[i]->cov));
+ est[i]->scale = xnmalloc (lag, sizeof (*est[i]->scale));
+ est[i]->coeff = xnmalloc (lag, sizeof (*est[i]->coeff));
+ est[i]->max_lag = (double) lag;
+ for (j = 0; j < lag; j++)
{
- *n_vars--;
-/* msg (MW, _("Cannot compute autocovariance for a non-numeric variable %s"), */
-/* var_to_string (vars[i])); */
+ est[i]->coeff[j] = xmalloc (sizeof (*(est[i]->coeff + j)));
}
}
- /*
- First data pass to get the mean and variance.
- */
- get_mean_variance (*n_vars, cf, est);
- get_covariance (*n_vars, cf, est, lag);
+ get_mean_variance (data, est);
+ get_covariance (data, est, lag);
+ get_coef (data, est, lag);
+
+ return est;
+}
+
+static void
+pspp_innovations_free_one (struct innovations_estimate *est)
+{
+ size_t i;
+
+ assert (est != NULL);
+ free (est->cov);
+ free (est->scale);
+ for (i = 0; i < (size_t) est->max_lag; i++)
+ {
+ pspp_coeff_free (est->coeff[i]);
+ }
+}
+
+void pspp_innovations_free (struct innovations_estimate **est, size_t n)
+{
+ size_t i;
+
+ assert (est != NULL);
+ for (i = 0; i < n; i++)
+ {
+ pspp_innovations_free_one (est[i]);
+ }
+ free (est);
}