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arma.c

/* 
 *  gretl -- Gnu Regression, Econometrics and Time-series Library
 *  Copyright (C) 2001 Allin Cottrell and Riccardo "Jack" Lucchetti
 * 
 *  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 3 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, see <http://www.gnu.org/licenses/>.
 */

#include "libgretl.h"
#include "libset.h"
#include "kalman.h"
#include "matrix_extra.h"
#include "gretl_bfgs.h"
#include "arma_priv.h"

#include "../cephes/libprob.h"

#define ARMA_DEBUG 0
#define ARMA_MDEBUG 0

#include "arma_common.c"

#define KALMAN_ALL 999

00035 struct bchecker {
    int qmax;
    double *temp;
    double *tmp2;
    cmplx *roots;
};

static void bchecker_free (struct bchecker *b)
{
    if (b != NULL) {
      free(b->temp);
      free(b->tmp2);
      free(b->roots);
      free(b);
    }
}

static struct bchecker *bchecker_allocate (arma_info *ainfo)
{
    struct bchecker *b;

    b = malloc(sizeof *b);
    if (b == NULL) {
      return NULL;
    }

    b->temp = NULL;
    b->tmp2 = NULL;
    b->roots = NULL;

    b->qmax = ainfo->q + ainfo->Q * ainfo->pd;

    b->temp  = malloc((b->qmax + 1) * sizeof *b->temp);
    b->tmp2  = malloc((b->qmax + 1) * sizeof *b->tmp2);
    b->roots = malloc(b->qmax * sizeof *b->roots);

    if (b->temp == NULL || b->tmp2 == NULL || b->roots == NULL) {
      bchecker_free(b);
      b = NULL;
    } 

    return b;
}

/* check whether the MA estimates have gone out of bounds in the
   course of iteration */

int ma_out_of_bounds (arma_info *ainfo, const double *theta,
                  const double *Theta)
{
    static struct bchecker *b = NULL;
    double re, im, rt;
    int i, j, k, m, si, qtot;
    int tzero = 1, Tzero = 1;
    int err = 0, cerr = 0;

    if (ainfo == NULL) {
      /* signal for cleanup */
      bchecker_free(b);
      b = NULL;
      return 0;
    }

    k = 0;
    for (i=0; i<ainfo->q && tzero; i++) {
      if (MA_included(ainfo, i)) {
          if (theta[k++] != 0.0) {
            tzero = 0;
          }
      }
    }  

    for (i=0; i<ainfo->Q && Tzero; i++) {
      if (Theta[i] != 0.0) {
          Tzero = 0;
      }    
    }  
    
    if (tzero && Tzero) {
      /* nothing to be done */
      return 0;
    }

    if (b == NULL) {
      b = bchecker_allocate(ainfo);
      if (b == NULL) {
          return 1;
      }
    }

    b->temp[0] = 1.0;

    /* initialize to non-seasonal MA or zero */
    k = 0;
    for (i=0; i<b->qmax; i++) {
        if (i < ainfo->q && MA_included(ainfo, i)) {
          b->temp[i+1] = theta[k++];
        } else {
            b->temp[i+1] = 0.0;
        }
    }

    /* add seasonal MA and interaction */
    if (Tzero) {
      qtot = ainfo->q;
    } else {
      qtot = b->qmax;
      for (j=0; j<ainfo->Q; j++) {
          si = (j + 1) * ainfo->pd;
          b->temp[si] += Theta[j];
          k = 0;
          for (i=0; i<ainfo->q; i++) {
            if (MA_included(ainfo, i)) {
                m = si + (i + 1);
                b->temp[m] += Theta[j] * theta[k++];
            } 
          }
      }
    }

#if ARMA_DEBUG
    if (b->temp[qtot] == 0.0) {
      fprintf(stderr, "b->temp[%d] = 0; polrt won't work\n", qtot);
      fprintf(stderr, "q = %d, Q = %d, b->qmax = %d\n", 
            ainfo->q, ainfo->Q, b->qmax);
      for (i=0; i<=qtot; i++) {
          fprintf(stderr, "b->temp[%d] = %g\n", i, b->temp[i]);
      }
    }
#endif

    cerr = polrt(b->temp, b->tmp2, qtot, b->roots);
    if (cerr) {
      fprintf(stderr, "ma_out_of_bounds: polrt returned %d\n", cerr);
      return 0; /* ?? */
    }

    for (i=0; i<qtot; i++) {
      re = b->roots[i].r;
      im = b->roots[i].i;
      rt = re * re + im * im;
      if (rt > DBL_EPSILON && rt <= 1.0) {
          pprintf(ainfo->prn, "MA root %d = %g\n", i, rt);
          err = 1;
          break;
      }
    }

    return err;
}

void bounds_checker_cleanup (void)
{
    ma_out_of_bounds(NULL, NULL, NULL);
}

/*
  Given an ARMA process $A(L)B(L) y_t = C(L)D(L) \epsilon_t$, finds the 
  roots of the four polynomials -- or just two polynomials if seasonal
  AR and MA effects, B(L) and D(L) are not present -- and attaches
  this information to the ARMA model.

  pmod: MODEL pointer to which the roots info should be attached.

  ainfo: gives various pieces of information on the ARMA model,
  including seasonal and non-seasonal AR and MA orders.

  coeff: ifc + p + q + P + Q vector of coefficients (if an intercept
  is present it is element 0 and is ignored)

  returns: zero on success, non-zero on failure
*/

int arma_model_add_roots (MODEL *pmod, arma_info *ainfo,
                    const double *coeff)
{
    const double *phi =   coeff + ainfo->ifc;
    const double *Phi =     phi + ainfo->np;
    const double *theta =   Phi + ainfo->P;
    const double *Theta = theta + ainfo->nq;
    int nr = ainfo->p + ainfo->P + ainfo->q + ainfo->Q;
    int pmax, qmax, lmax;
    double *temp = NULL, *tmp2 = NULL;
    cmplx *rptr, *roots = NULL;
    int i, k, cerr = 0;

    pmax = (ainfo->p > ainfo->P)? ainfo->p : ainfo->P;
    qmax = (ainfo->q > ainfo->Q)? ainfo->q : ainfo->Q;
    lmax = (pmax > qmax)? pmax : qmax;

    if (pmax == 0 && qmax == 0) {
      return 0;
    }

    temp = malloc((lmax + 1) * sizeof *temp);
    tmp2 = malloc((lmax + 1) * sizeof *tmp2);
    roots = malloc(nr * sizeof *roots);

    if (temp == NULL || tmp2 == NULL || roots == NULL) {
      free(temp);
      free(tmp2);
      free(roots);
      return E_ALLOC;
    }

    temp[0] = 1.0;
    rptr = roots;

    if (ainfo->p > 0) {
      /* A(L), non-seasonal */
      k = 0;
      for (i=0; i<ainfo->p; i++) {
          if (AR_included(ainfo, i)) {
            temp[i+1] = -phi[k++];
          } else {
            temp[i+1] = 0;
          }
      }
      cerr = polrt(temp, tmp2, ainfo->p, rptr);
      rptr += ainfo->p;
    }

    if (!cerr && ainfo->P > 0) {
      /* B(L), seasonal */
      for (i=0; i<ainfo->P; i++) {
          temp[i+1] = -Phi[i];
      }    
      cerr = polrt(temp, tmp2, ainfo->P, rptr);
      rptr += ainfo->P;
    }

    if (!cerr && ainfo->q > 0) {
      /* C(L), non-seasonal */
      k = 0;
      for (i=0; i<ainfo->q; i++) {
          if (MA_included(ainfo, i)) {
            temp[i+1] = theta[k++];
          } else {
            temp[i+1] = 0;
          }
      }  
      cerr = polrt(temp, tmp2, ainfo->q, rptr);
      rptr += ainfo->q;
    }

    if (!cerr && ainfo->Q > 0) {
      /* D(L), seasonal */
      for (i=0; i<ainfo->Q; i++) {
          temp[i+1] = Theta[i];
      }  
      cerr = polrt(temp, tmp2, ainfo->Q, rptr);
    }
    
    free(temp);
    free(tmp2);

    if (cerr) {
      free(roots);
    } else {
      gretl_model_set_data(pmod, "roots", roots, GRETL_TYPE_CMPLX_ARRAY,
                       nr * sizeof *roots);
    }

    return 0;
}

/* below: exact ML using Kalman filter apparatus */

typedef struct kalman_helper_ khelper;

00305 struct kalman_helper_ {
    gretl_matrix_block *B;
    gretl_matrix *S;
    gretl_matrix *P;
    gretl_matrix *F;
    gretl_matrix *A;
    gretl_matrix *H;
    gretl_matrix *Q;
    gretl_matrix *E;
    gretl_matrix *Svar;

    gretl_matrix *Svar2;
    gretl_matrix *vQ;

    gretl_matrix *F_; /* used only for ARIMA via levels */
    gretl_matrix *Q_; /* ditto */
    gretl_matrix *P_; /* ditto */

    arma_info *kainfo; 
};

static void kalman_helper_free (khelper *kh)
{
    if (kh != NULL) {
      gretl_matrix_block_destroy(kh->B);
      gretl_matrix_free(kh->Svar2);
      gretl_matrix_free(kh->vQ);
      gretl_matrix_free(kh->F_);
      gretl_matrix_free(kh->Q_);
      gretl_matrix_free(kh->P_);
      free(kh);
    }
}

static khelper *kalman_helper_new (arma_info *ainfo,
                           int r, int k)
{
    khelper *kh;
    int r0, r2;
    int err = 0;

    kh = malloc(sizeof *kh);
    if (kh == NULL) {
      return NULL;
    }

    r0 = ainfo->r0;
    r2 = r0 * r0;

    kh->Svar2 = kh->vQ = NULL;
    kh->F_ = kh->Q_ = kh->P_ = NULL;

    kh->B = gretl_matrix_block_new(&kh->S, r, 1,
                           &kh->P, r, r,
                           &kh->F, r, r,
                           &kh->A, k, 1,
                           &kh->H, r, 1,
                           &kh->Q, r, r,
                           &kh->E, ainfo->fullT, 1,
                           &kh->Svar, r2, r2,
                           NULL);

    if (kh->B == NULL) {
      err = E_ALLOC;
    } else if (arma_using_vech(ainfo)) {
      int m = r0 * (r0 + 1) / 2;

      kh->Svar2 = gretl_matrix_alloc(m, m);
      kh->vQ = gretl_column_vector_alloc(m);
      if (kh->Svar2 == NULL || kh->vQ == NULL) {
          err = E_ALLOC;
      }         
    } else {
      kh->vQ = gretl_column_vector_alloc(r2);
      if (kh->vQ == NULL) {
          err = E_ALLOC;
      }
    }

    if (!err && arima_levels(ainfo)) {
      kh->F_ = gretl_matrix_alloc(r0, r0);
      kh->Q_ = gretl_matrix_alloc(r0, r0);
      kh->P_ = gretl_matrix_alloc(r0, r0);
      if (kh->F_ == NULL || kh->Q_ == NULL || kh->P_ == NULL) {
          err = E_ALLOC;
      }
    }

    if (err) {
      kalman_helper_free(kh);
      kh = NULL;
    } else {
      kh->kainfo = ainfo;
    }

    return kh;
}

/* Get the dimension of the state-space representation: note
   that this is augmented if we're estimating an ARIMA
   model using the levels formulation.
*/

static int ainfo_get_state_size (arma_info *ainfo)
{
    int pmax = ainfo->p + ainfo->pd * ainfo->P;
    int qmax = ainfo->q + ainfo->pd * ainfo->Q;
    int r = (pmax > qmax + 1)? pmax : qmax + 1;

    ainfo->r0 = r;

    if (arima_levels(ainfo)) {
      r += ainfo->d + ainfo->pd * ainfo->D;
    }

    return r;
}

static int allocate_ac_mc (arma_info *ainfo)
{
    int m = (ainfo->P > 0) + (ainfo->Q > 0);
    int err = 0;

    if (m > 0) {
      double *ac = NULL, *mc = NULL;
      int n, i = 0;

      ainfo->aux = doubles_array_new(m, 0);
      if (ainfo->aux == NULL) {
          return E_ALLOC;
      }

      if (ainfo->P > 0) {
          n = 1 + ainfo->p + ainfo->pd * ainfo->P;
          ac = malloc(n * sizeof *ac);
          if (ac == NULL) {
            err = E_ALLOC;
          } else {
            ainfo->aux[i++] = ac;
          }
      }

      if (!err && ainfo->Q > 0) {
          n = 1 + ainfo->q + ainfo->pd * ainfo->Q;
          mc = malloc(n * sizeof *mc);
          if (mc == NULL) {
            err = E_ALLOC;
          } else {
            ainfo->aux[i++] = mc;
          }
      }

      if (err) {
          doubles_array_free(ainfo->aux, m);
      } else {
          ainfo->n_aux = m;
      }
    }

    return err;
}

static void write_big_phi (const double *phi, 
                     const double *Phi,
                     arma_info *ainfo,
                     gretl_matrix *F)
{
    int pmax = ainfo->p + ainfo->pd * ainfo->P;
    double *ac = ainfo->aux[0];
    double x, y;
    int i, j, k, ii;

    for (i=0; i<=pmax; i++) {
      ac[i] = 0.0;
    }

    for (j=-1; j<ainfo->P; j++) {
      x = (j < 0)? -1 : Phi[j];
      k = 0.0;
      for (i=-1; i<ainfo->p; i++) {
          if (i < 0) {
            y = -1;
          } else if (AR_included(ainfo, i)) {
            y = phi[k++];
          } else {
            y = 0.0;
          }
          ii = (j+1) * ainfo->pd + (i+1);
          ac[ii] -= x * y;
      }
    }

    for (i=0; i<pmax; i++) {
      gretl_matrix_set(F, 0, i, ac[i+1]);
    }
}

static void write_big_theta (const double *theta, 
                       const double *Theta,
                       arma_info *ainfo,
                       gretl_matrix *H,
                       gretl_matrix *F)
{
    int qmax = ainfo->q + ainfo->pd * ainfo->Q;
    int i = (ainfo->P > 0)? 1 : 0;
    double *mc = ainfo->aux[i];
    double x, y;
    int j, k, ii;

    for (i=0; i<=qmax; i++) {
      mc[i] = 0.0;
    }

    for (j=-1; j<ainfo->Q; j++) {
      x = (j < 0)? 1 : Theta[j];
      k = 0;
        for (i=-1; i<ainfo->q; i++) {
          if (i < 0) {
            y = 1;
          } else if (MA_included(ainfo, i)) {
            y = theta[k++];
          } else {
            y = 0;
          }
            ii = (j+1) * ainfo->pd + (i+1);
          mc[ii] = x * y;
        }
    }

    for (i=1; i<=qmax; i++) {
      if (H != NULL) {
          H->val[i] = mc[i];
      } else {
          gretl_matrix_set(F, ainfo->r0, i, mc[i]);
      }
    }
}

static void condense_row (gretl_matrix *targ,
                    const gretl_matrix *src,
                    int targrow, int srcrow,
                    int n)
{
    double x;
    int i, j, k, g;
    int targcol = 0;

    for (j=0; j<n; j++) {
      for (i=j; i<n; i++) {
          k = j * n + i;
          g = (k % n) * n + k / n;
          x = gretl_matrix_get(src, srcrow, k);
          if (g != k) {
            x += gretl_matrix_get(src, srcrow, g);
          } 
          gretl_matrix_set(targ, targrow, targcol++, x);
      }
    }
}

static void condense_state_vcv (gretl_matrix *targ, 
                        const gretl_matrix *src,
                        int n)
{
    int posr = 0, posc = 0;
    int i, j;

    for (i=0; i<n; i++) {
      for (j=0; j<n; j++) {
          if (j >= i) {
            condense_row(targ, src, posr++, posc, n);
          }
          posc++;
      }
    }
}

static int kalman_matrices_init (arma_info *ainfo,
                         khelper *kh,
                         const double *y)
{
    int r0 = ainfo->r0;
    int r = kh->F->rows;

    gretl_matrix_zero(kh->A);
    gretl_matrix_zero(kh->S);
    gretl_matrix_zero(kh->P);
 
    gretl_matrix_zero(kh->F);
    gretl_matrix_inscribe_I(kh->F, 1, 0, r0 - 1);

    gretl_matrix_zero(kh->Q);
    gretl_matrix_set(kh->Q, 0, 0, 1.0);

    gretl_matrix_zero(kh->H);
    gretl_vector_set(kh->H, 0, 1.0);

    if (arima_levels(ainfo)) {
      /* write additional constant elements of F, H and S */
      int d = ainfo->d, D = ainfo->D;
      int s = ainfo->pd;
      int i, k = d + s * D;
      int *c = arima_delta_coeffs(d, D, s);
      double y0;

      if (c == NULL) {
          return E_ALLOC;
      }
      for (i=0; i<k; i++) {
          gretl_matrix_set(kh->F, r0, r0 + i, c[i]);
      }
      gretl_matrix_set(kh->F, r0, 0, 1.0);
      if (r - r0 > 1) {
          gretl_matrix_inscribe_I(kh->F, r0 + 1, r0, k - 1);
      }
      for (i=0; i<k; i++) {
          gretl_vector_set(kh->H, r0 + i, c[i]);
          y0 = y[ainfo->t1 - 1 - i];
          if (ainfo->yscale != 1.0 && !na(y0)) {
            y0 *= ainfo->yscale;
          }
          gretl_vector_set(kh->S, r0 + i, y0);
      }
      free(c);

#if ARMA_DEBUG
      gretl_matrix_print(kh->S, "S0 (arima via levels)");
#endif

      /* and initialize the plain-arma "shadow" matrices */
      gretl_matrix_zero(kh->F_);
      gretl_matrix_inscribe_I(kh->F_, 1, 0, r0 - 1);
      gretl_matrix_zero(kh->Q_);
      gretl_matrix_set(kh->Q_, 0, 0, 1.0);
      gretl_matrix_zero(kh->P_);
    }

    return 0;
}

static int write_kalman_matrices (khelper *kh,
                          const double *b, 
                          int idx)
{
    arma_info *ainfo = kh->kainfo;
    const double *phi =       b + ainfo->ifc;
    const double *Phi =     phi + ainfo->np;
    const double *theta =   Phi + ainfo->P;
    const double *Theta = theta + ainfo->nq;
    const double *beta =  Theta + ainfo->Q;
    double mu = (ainfo->ifc)? b[0] : 0.0;
    int rewrite_A = 0;
    int rewrite_F = 0;
    int rewrite_H = 0;
    int i, k, err = 0;

    if (idx == KALMAN_ALL) {
      rewrite_A = rewrite_F = rewrite_H = 1;
    } else {
      /* called in context of calculating score */
      int pmax = ainfo->ifc + ainfo->np + ainfo->P;
      int tmax = pmax + ainfo->nq + ainfo->Q;

      if (ainfo->ifc && idx == 0) {
          rewrite_A = 1;
      } else if (idx >= ainfo->ifc && idx < pmax) {
          rewrite_F = 1;
      } else if (idx >= ainfo->ifc && idx < tmax) {
          rewrite_H = 1;
      } else {
          rewrite_A = 1;
      }
    }

#if ARMA_MDEBUG
    fprintf(stderr, "\n*** write_kalman_matrices: before\n");
    gretl_matrix_print(kh->A, "A");
    gretl_matrix_print(kh->F, "F");
    gretl_matrix_print(kh->H, "H");
    gretl_matrix_print(kh->P, "P");
#endif 

    /* See Hamilton, Time Series Analysis, ch 13, p. 375 */

    if (rewrite_A) {
      /* const and coeffs on exogenous vars */
      gretl_vector_set(kh->A, 0, mu);
      for (i=0; i<ainfo->nexo; i++) {
          gretl_vector_set(kh->A, i + 1, beta[i]);
      }
    }

    if (rewrite_H) {
      /* form the H vector using theta and/or Theta */
      if (ainfo->Q > 0) {
          write_big_theta(theta, Theta, ainfo, kh->H, NULL);
      } else {
          k = 0;
          for (i=0; i<ainfo->q; i++) {
            if (MA_included(ainfo, i)) {
                gretl_vector_set(kh->H, i+1, theta[k++]);
            } else {
                gretl_vector_set(kh->H, i+1, 0.0);
            }
          }
      }
    }

    if (rewrite_F) {
      /* form the F matrix using phi and/or Phi */
      gretl_matrix *F = (kh->F_ != NULL)? kh->F_ : kh->F;
      gretl_matrix *Q = (kh->Q_ != NULL)? kh->Q_ : kh->Q;
      gretl_matrix *P = (kh->P_ != NULL)? kh->P_ : kh->P;

      if (ainfo->P > 0) {
          write_big_phi(phi, Phi, ainfo, F);
      } else {
          k = 0;
          for (i=0; i<ainfo->p; i++) {
            if (AR_included(ainfo, i)) {
                gretl_matrix_set(F, 0, i, phi[k++]);
            } else {
                gretl_matrix_set(F, 0, i, 0.0);
            }
          }
      }

      if (arima_levels(ainfo)) {
          /* the full F matrix incorporates \theta */
          if (ainfo->Q > 0) {
            write_big_theta(theta, Theta, ainfo, NULL, kh->F);
          } else {
            k = 0;
            for (i=0; i<ainfo->q; i++) {
                if (MA_included(ainfo, i)) {
                  gretl_matrix_set(kh->F, ainfo->r0, i+1, theta[k++]);
                } else {
                  gretl_matrix_set(kh->F, ainfo->r0, i+1, 0.0);
                }
            }           
          }
      }

      /* form $P_{1|0}$ (MSE) matrix, as per Hamilton, ch 13, p. 378. */

      gretl_matrix_kronecker_product(F, F, kh->Svar);
      gretl_matrix_I_minus(kh->Svar);

      if (arma_using_vech(ainfo)) {
          condense_state_vcv(kh->Svar2, kh->Svar, gretl_matrix_rows(F));
          gretl_matrix_vectorize_h(kh->vQ, Q);
          err = gretl_LU_solve(kh->Svar2, kh->vQ);
          if (!err) {
            gretl_matrix_unvectorize_h(P, kh->vQ);
          }
      } else {
          gretl_matrix_vectorize(kh->vQ, Q);
          err = gretl_LU_solve(kh->Svar, kh->vQ);
          if (!err) {
            gretl_matrix_unvectorize(P, kh->vQ);
          }
      }
    }

    if (arima_levels(ainfo)) {
      /* complete the job on F, Q, P and S */
      gretl_matrix_inscribe_matrix(kh->F, kh->F_, 0, 0, GRETL_MOD_NONE);
      gretl_matrix_inscribe_matrix(kh->Q, kh->Q_, 0, 0, GRETL_MOD_NONE);
      gretl_matrix_inscribe_matrix(kh->P, kh->P_, 0, 0, GRETL_MOD_NONE);
    }

#if ARMA_MDEBUG
    fprintf(stderr, "\n*** after\n");
    gretl_matrix_print(kh->A, "A");
    gretl_matrix_print(kh->F, "F");
    gretl_matrix_print(kh->H, "H");
    gretl_matrix_print(kh->P, "P");
#endif    

    return err;
}

static int rewrite_kalman_matrices (kalman *K, const double *b, int i)
{
    khelper *kh = (khelper *) kalman_get_data(K);
    int err = write_kalman_matrices(kh, b, i);

    if (!err) {
      kalman_set_initial_state_vector(K, kh->S);
      kalman_set_initial_MSE_matrix(K, kh->P);
    }

    return err;
}

static const double *kalman_arma_llt_callback (const double *b, int i, 
                                     void *data)
{
    kalman *K = (kalman *) data;
    khelper *kh = kalman_get_data(K);
    int err;

    rewrite_kalman_matrices(K, b, i);
    err = kalman_forecast(K, NULL);

#if ARMA_DEBUG
    fprintf(stderr, "kalman_arma_llt: kalman f'cast gave "
          "err = %d, ll = %#.12g\n", err, kalman_get_loglik(K));
#endif

    return (err)? NULL : kh->E->val;
}

/* add covariance matrix and standard errors based on Outer Product of
   Gradient
*/

static int arma_OPG_vcv (MODEL *pmod, kalman *K, double *b, 
                   double s2, int k, int T,
                   PRN *prn)
{
    gretl_matrix *G = NULL;
    gretl_matrix *V = NULL;
    double rcond;
    int err = 0;

    G = numerical_score_matrix(b, k, T, kalman_arma_llt_callback, 
                         K, &err);
    if (err) {
      goto bailout;
    }

    V = gretl_matrix_alloc(k, k);
    if (V == NULL) {
      err = E_ALLOC;
      goto bailout;
    }

    gretl_matrix_multiply_mod(G, GRETL_MOD_NONE,
                        G, GRETL_MOD_TRANSPOSE,
                        V, GRETL_MOD_NONE);

    rcond = gretl_symmetric_matrix_rcond(V, &err);
    if (!err && rcond < 1.0E-10) {
      pprintf(prn, "OPG: rcond = %g; will try Hessian\n", rcond);
      err = 1;
    }

    if (!err) {
      err = gretl_invert_symmetric_matrix(V);
    }

    if (!err) {
      gretl_matrix_multiply_by_scalar(V, s2);
      err = gretl_model_write_vcv(pmod, V, -1);
    }

 bailout:

    gretl_matrix_free(G);
    gretl_matrix_free(V);
    
    return err;
}

#if ARMA_DEBUG

static void debug_print_theta (const double *theta,
                         const double *Theta,
                         arma_info *ainfo)
{
    int i, k = 0;

    fprintf(stderr, "kalman_arma_ll():\n");

    for (i=0; i<ainfo->q; i++) {
      if (MA_included(ainfo, i)) {
          fprintf(stderr, "theta[%d] = %#.12g\n", i+1, theta[k++]);
      }
    }

    for (i=0; i<ainfo->Q; i++) {
      fprintf(stderr, "Theta[%d] = %#.12g\n", i, Theta[i]);
    }   
}

#endif

static int kalman_do_ma_check = 1;

static double kalman_arma_ll (const double *b, void *data)
{
    kalman *K = (kalman *) data;
    khelper *kh = kalman_get_data(K);
    arma_info *ainfo = kh->kainfo;
    int offset = ainfo->ifc + ainfo->np + ainfo->P;
    const double *theta = b + offset;
    const double *Theta = theta + ainfo->nq;
    double ll = NADBL;
    int err = 0;

#if ARMA_DEBUG
    debug_print_theta(theta, Theta, ainfo);
#endif

    if (kalman_do_ma_check && ma_out_of_bounds(ainfo, theta, Theta)) {
      pputs(kalman_get_printer(K), "arma: MA estimate(s) out of bounds\n");
      return NADBL;
    }

    err = rewrite_kalman_matrices(K, b, KALMAN_ALL);

    if (!err) {
      err = kalman_forecast(K, NULL);
      ll = kalman_get_loglik(K);
#if ARMA_DEBUG
      fprintf(stderr, "kalman_arma_ll: kalman_forecast gave %d, "
            "loglik = %#.12g\n", err, ll);
#endif

    }

    return ll;
}

static int arima_ydiff_only (arma_info *ainfo)
{
    if ((ainfo->d > 0 || ainfo->D > 0) &&
      ainfo->nexo > 0 && !arma_xdiff(ainfo)) {
      return 1;
    } else {
      return 0;
    }
}

static int arma_use_hessian (gretlopt opt)
{
    int ret = 1;

    if (opt & OPT_G) {
      ret = 0;
    } else if (libset_get_int(ARMA_VCV) == VCV_OP) {
      ret = 0;
    }

    return ret;
}

static void arma_add_ehat (MODEL *pmod, arma_info *ainfo,
                     kalman *K, double *b)
{
    int err;

    kalman_set_options(K, KALMAN_ETT);
    rewrite_kalman_matrices(K, b, KALMAN_ALL);
    err = kalman_forecast(K, NULL);

    if (!err) {
      khelper *kh = kalman_get_data(K);
      gretl_matrix *ehat = gretl_matrix_copy(kh->E);

      if (ehat != NULL) {
          ehat->t1 = pmod->t1;
          ehat->t2 = pmod->t2;
          gretl_model_set_matrix_as_data(pmod, "ehat", ehat);
      }
    }
}

static int kalman_arma_finish (MODEL *pmod, arma_info *ainfo,
                         const double **Z, const DATAINFO *pdinfo, 
                         kalman *K, double *b, 
                         gretlopt opt, PRN *prn)
{
    khelper *kh = kalman_get_data(K);
    int do_hess = arma_use_hessian(opt);
    int kopt, i, t, k = ainfo->nc;
    double s2;
    int err;

    pmod->t1 = ainfo->t1;
    pmod->t2 = ainfo->t2;
    pmod->nobs = ainfo->T;
    pmod->ncoeff = ainfo->nc;
    pmod->full_n = pdinfo->n;

    /* in the Kalman case the basic model struct is empty, so we 
       have to allocate for coefficients, residuals and so on
    */

    err = gretl_model_allocate_storage(pmod);
    if (err) {
      return err;
    }

    for (i=0; i<k; i++) {
      pmod->coeff[i] = b[i];
    }

    i = 0;
    for (t=pmod->t1; t<=pmod->t2; t++) {
      pmod->uhat[t] = gretl_vector_get(kh->E, i++);
    }

    s2 = kalman_get_arma_variance(K);
    pmod->sigma = sqrt(s2);

    pmod->lnL = kalman_get_loglik(K);
    kopt = kalman_get_options(K);

    /* rescale if we're using average loglikelihood */
    if (kopt & KALMAN_AVG_LL) {
      pmod->lnL *= ainfo->T;
    }

    if (opt & OPT_E) {
      arma_add_ehat(pmod, ainfo, K, b);
    }

#if ARMA_DEBUG
    fprintf(stderr, "kalman_arma_finish: doing VCV, method %s\n",
          (do_hess)? "Hessian" : "OPG");
#endif

    if (!do_hess) {
      /* try OPG first, hessian as fallback */
      err = arma_OPG_vcv(pmod, K, b, s2, k, ainfo->T, prn);
      if (err) {
          err = 0;
          do_hess = 1;
      } else {
          gretl_model_set_vcv_info(pmod, VCV_ML, VCV_OP);
          pmod->opt |= OPT_G;
      }
    } 

    if (do_hess) { 
      gretl_matrix *Hinv;

      kalman_do_ma_check = 0;
      Hinv = numerical_hessian_inverse(b, ainfo->nc, kalman_arma_ll, 
                               K, &err);
      kalman_do_ma_check = 1;
      if (!err) {
          if (kopt & KALMAN_AVG_LL) {
            gretl_matrix_divide_by_scalar(Hinv, ainfo->T);
          }
          err = gretl_model_write_vcv(pmod, Hinv, -1);
          if (!err) {
            gretl_model_set_vcv_info(pmod, VCV_ML, VCV_HESSIAN);
          }
      }
      gretl_matrix_free(Hinv);
    }

    if (!err) {
      write_arma_model_stats(pmod, ainfo, Z, pdinfo);
      arma_model_add_roots(pmod, ainfo, b);
      gretl_model_set_int(pmod, "arma_flags", ARMA_EXACT);
      if (arma_lbfgs(ainfo)) {
          pmod->opt |= OPT_L;
      }
      if (arima_ydiff_only(ainfo)) {
          pmod->opt |= OPT_Y;
      }
    }

#if 0 /* experimental: run the Koopman-style disturbance smoother
       after ARMA estimation
      */
    if (!err) {
      gretl_matrix *S, *U, *smu;
      int t;

      smu = gretl_column_vector_alloc(ainfo->T);

      kalman_set_initial_state_vector(K, kh->S);
      kalman_set_initial_MSE_matrix(K, kh->P);

      /* OR: rewrite_kalman_matrices(K, b, KALMAN_ALL); ? */
      S = kalman_smooth(K, NULL, &U, &err);

      fprintf(stderr, "kalman_smooth: err = %d\n", err);
      gretl_matrix_print(S, "S");
      gretl_matrix_print(U, "U");

      i = 0;
      for (t=ainfo->t1; t<=ainfo->t2; t++) {
          double u = gretl_matrix_get(S, i, 0);

          /* specific to ARMA(1,1) ? */
          u -= b[0] * gretl_matrix_get(S, i, 1);
          fprintf(stderr, "%#10.5g\n", u);
          if (i > 0) {
            gretl_vector_set(smu, i, gretl_matrix_get(U, i-1, 0));
          } else {
            gretl_vector_set(smu, i, u);
          }
          i++;
      }

      gretl_matrix_write_as_text(smu, "smu.mat");

      gretl_matrix_free(S);
      gretl_matrix_free(U);
      gretl_matrix_free(smu);
    }
#endif

#if 0 /* not ready yet: after estimation of ARMA with missing
         values, use the Kalman smoother to estimate the
       missing data
      */
    if (!err && arma_missvals(ainfo)) {
      gretl_matrix *ys = kalman_arma_smooth(K, &err);
      int t;

      i = 0;
      for (t=ainfo->t1; t<=ainfo->t2; t++) {
          if (na(pmod->yhat[t])) {
            pmod->yhat[t] = gretl_vector_get(ys, i);
          } else {
            fprintf(stderr, "%g vs %g\n", pmod->yhat[t], ys->val[i]);
          }
          i++;
      }
      gretl_matrix_free(ys);
    }
#endif

    return err;
}

static void kalman_rescale_y (gretl_vector *y, double scale)
{
    int i;

#if ARMA_DEBUG
    fprintf(stderr, "kalman_rescale_y: multiplying by %g\n", scale);
#endif

    for (i=0; i<y->rows; i++) {
      if (!na(y->val[i])) {
          y->val[i] *= scale;
      }
    }
}

static void matrix_NA_to_nan (gretl_matrix *m)
{
    int i, n = m->rows * m->cols;

    for (i=0; i<n; i++) {
      if (na(m->val[i])) {
          m->val[i] = M_NA;
      }
    }
}

/* for Kalman: convert from full-length y series to
   y vector of length ainfo->T */

static gretl_matrix *form_arma_y_vector (arma_info *ainfo,
                               const double **Z,
                               int *err)
{
    gretl_matrix *yvec;

    yvec = gretl_vector_from_series(ainfo->y, ainfo->t1, ainfo->t2);

    if (yvec == NULL) {
      *err = E_ALLOC;
    } else {
      if (ainfo->yscale != 1.0) {
          kalman_rescale_y(yvec, ainfo->yscale);
      }
      if (arma_missvals(ainfo)) {
          matrix_NA_to_nan(yvec);
      }
#if ARMA_DEBUG
      gretl_matrix_print(yvec, "arma y vector");
#endif
    }
    
    return yvec;
}

static gretl_matrix *form_arma_X_matrix (arma_info *ainfo,
                               const double **Z,
                               int *err)
{
    gretl_matrix *X;
    int missop;

#if ARMA_DEBUG
    printlist(ainfo->xlist, "ainfo->xlist (exog vars)");
#endif

    if (arma_na_ok(ainfo)) {
      missop = M_MISSING_OK;
    } else {
      missop = M_MISSING_ERROR;
    }

    X = gretl_matrix_data_subset(ainfo->xlist, Z, ainfo->t1, ainfo->t2, 
                         missop, err);

#if ARMA_DEBUG
    gretl_matrix_print(X, "X");
#endif

    return X;
}

static int kalman_undo_y_scaling (arma_info *ainfo,
                          gretl_matrix *y, double *b, 
                          kalman *K)
{
    double *beta = b + 1 + ainfo->np + ainfo->P +
      ainfo->nq + ainfo->Q;
    int i, t, T = ainfo->t2 - ainfo->t1 + 1;
    int err = 0;

    b[0] /= ainfo->yscale;

    for (i=0; i<ainfo->nexo; i++) {
      beta[i] /= ainfo->yscale;
    }

    i = ainfo->t1;
    for (t=0; t<T; t++) {
      y->val[t] /= ainfo->yscale;
    }

    if (na(kalman_arma_ll(b, K))) {
      err = 1;
    }

    return err;
}

static void free_arma_X_matrix (arma_info *ainfo, gretl_matrix *X)
{
    if (X == ainfo->dX) {
      gretl_matrix_free(ainfo->dX);
      ainfo->dX = NULL;
    } else {
      gretl_matrix_free(X);
    }
}

static int kalman_arma (double *coeff, 
                  const double **Z, const DATAINFO *pdinfo,
                  arma_info *ainfo, MODEL *pmod,
                  gretlopt opt)
{
    kalman *K = NULL;
    khelper *kh = NULL;
    gretl_matrix *y = NULL;
    gretl_matrix *X = NULL;
    int r, k = 1 + ainfo->nexo; /* number of exog vars plus space for const */
    int fncount = 0, grcount = 0;
    int use_newton = 0;
    double *b;
    int i, err = 0;
    
    b = malloc(ainfo->nc * sizeof *b);
    if (b == NULL) {
      return E_ALLOC;
    }

    for (i=0; i<ainfo->nc; i++) {
      b[i] = coeff[i];
    }

#if ARMA_DEBUG
    fputs("initial coefficients:\n", stderr);
    for (i=0; i<ainfo->nc; i++) {
      fprintf(stderr, " b[%d] = % .10E\n", i, b[i]);
    }
#endif

    y = form_arma_y_vector(ainfo, Z, &err);

    if (!err && ainfo->nexo > 0) {
      if (ainfo->dX != NULL) {
          X = ainfo->dX;
      } else {
          X = form_arma_X_matrix(ainfo, Z, &err);
      }
    }

    if (!err) {
      err = allocate_ac_mc(ainfo);
    }

    if (err) {
      goto bailout;
    }

    r = ainfo_get_state_size(ainfo);

    /* when should we use vech apparatus? */
    if (r > 4) {
      set_arma_use_vech(ainfo);
    }

    kh = kalman_helper_new(ainfo, r, k);
    if (kh == NULL) {
      err = E_ALLOC;
      goto bailout;
    }

    kalman_matrices_init(ainfo, kh, Z[ainfo->yno]);

#if ARMA_DEBUG
    fprintf(stderr, "ready to estimate: ainfo specs:\n"
          "p=%d, P=%d, q=%d, Q=%d, ifc=%d, nexo=%d, t1=%d, t2=%d\n", 
          ainfo->p, ainfo->P, ainfo->q, ainfo->Q, ainfo->ifc, 
          ainfo->nexo, ainfo->t1, ainfo->t2);
    fprintf(stderr, "Kalman dims: r = %d, k = %d, T = %d, ncoeff=%d\n", 
          r, k, ainfo->T, ainfo->nc);
#endif

    K = kalman_new(kh->S, kh->P, kh->F, kh->A, kh->H, kh->Q, 
               NULL, y, X, NULL, kh->E, &err);

    if (err) {
      fprintf(stderr, "kalman_new(): err = %d\n", err);
    } else {
      double toler;
      int maxit;

      kalman_attach_printer(K, ainfo->prn);
      kalman_attach_data(K, kh);

      if (r > 3 && !arima_levels(ainfo)) {
          kalman_set_nonshift(K, 1);
      } else {
          kalman_set_nonshift(K, r);
      }

      if (arma_avg_ll(ainfo) || getenv("KALMAN_AVG_LL") != NULL) {
          kalman_set_options(K, KALMAN_ARMA_LL | KALMAN_AVG_LL);
      } else {
          kalman_set_options(K, KALMAN_ARMA_LL);
      }

      BFGS_defaults(&maxit, &toler, ARMA);

      if (libset_get_int(GRETL_OPTIM) == OPTIM_NEWTON ||
          getenv("ARMA_USE_NEWTON") != NULL) {
          use_newton = 1;
      }

      if (use_newton) {
          double crittol = 1.0e-7;
          double gradtol = 1.0e-7;

          err = newton_raphson_max(b, ainfo->nc, maxit, 
                             crittol, gradtol, &fncount, 
                             C_LOGLIK, kalman_arma_ll, 
                             NULL, NULL, K, opt, 
                             ainfo->prn);
      } else {
          int save_lbfgs = libset_get_bool(USE_LBFGS);

          if (save_lbfgs) {
            ainfo->pflags |= ARMA_LBFGS;
          } else if (opt & OPT_L) {
            libset_set_bool(USE_LBFGS, 1);
            ainfo->pflags |= ARMA_LBFGS;
          }
          
          err = BFGS_max(b, ainfo->nc, maxit, toler, 
                     &fncount, &grcount, kalman_arma_ll, C_LOGLIK,
                     NULL, K, NULL, opt, ainfo->prn);

          if (save_lbfgs == 0 && (opt & OPT_L)) {
            libset_set_bool(USE_LBFGS, 0);
          }
      }

      if (err) {
          fprintf(stderr, "kalman_arma: optimizer returned %d\n", err);
      } 
    }

    if (!err && ainfo->yscale != 1.0) {
      kalman_undo_y_scaling(ainfo, y, b, K);
    }

    if (!err) {
      if (use_newton) {
          gretl_model_set_int(pmod, "iters", fncount);
      } else {
          gretl_model_set_int(pmod, "fncount", fncount);
          gretl_model_set_int(pmod, "grcount", grcount);
      }
      err = kalman_arma_finish(pmod, ainfo, 
                         Z, pdinfo, K, b, 
                         opt, ainfo->prn);
    } 

 bailout:

    if (err) {
      pmod->errcode = err;
    }

    kalman_free(K);
    kalman_helper_free(kh);

    gretl_matrix_free(y);
    free_arma_X_matrix(ainfo, X);
    free(b);

    return err;
}

/* end of Kalman-specific material */

static int user_arma_init (double *coeff, arma_info *ainfo, int *init_done)
{
    PRN *prn = ainfo->prn;
    int i, nc = n_init_vals();

    if (nc == 0) {
      return 0;
    } else if (nc < ainfo->nc) {
      pprintf(prn, "ARMA initialization: need %d coeffs but got %d\n",
            ainfo->nc, nc);
      return E_DATA;
    }

    if (arma_exact_ml(ainfo)) {
      /* initialization is handled within BFGS/Newton-Raphson */
      for (i=0; i<ainfo->nc; i++) {
          coeff[i] = 0.0;
      }     
    } else {
      const gretl_matrix *m = get_init_vals();

      pprintf(prn, "\n%s: %s\n\n", _("ARMA initialization"), 
            _("user-specified values"));
            
      for (i=0; i<ainfo->nc; i++) {
          coeff[i] = gretl_vector_get(m, i);
      }
      free_init_vals();
    }

    *init_done = 1;

    return 0;
}

/* Should we try Hannan-Rissanen initialization of ARMA
   coefficients? */

static int prefer_hr_init (arma_info *ainfo)
{
    int ret = 0;

    if (ainfo->q > 1 || ainfo->Q > 0) {
      ret = 1;
      if (ainfo->pqspec != NULL && *ainfo->pqspec != '\0') {
          /* don't use for gappy arma (yet?) */
          ret = 0;
      } else if (arma_xdiff(ainfo)) {
          /* don't use for ARIMAX (yet?) */
          ret = 0;
      } else if (ainfo->T < 100) {
          /* unlikely to work well with small sample */
          ret = 0;
      } else if (ainfo->p > 0 && ainfo->P > 0) {
          /* not sure about this: HR catches the MA terms, but NLS
             handles the seasonal/non-seasonal AR interactions better
          */
          ret = 0;
      } else if ((ainfo->P > 0 && ainfo->p >= ainfo->pd) ||
               (ainfo->Q > 0 && ainfo->q >= ainfo->pd)) {
          /* overlapping seasonal/non-seasonal orders screw things up */
          ret = 0;
      } else if (ret && arma_exact_ml(ainfo)) {
          /* screen for cases where we'll use NLS */
          if (ainfo->P > 0) {
            ret = 0;
          } else if (ainfo->p + ainfo->P > 0 && ainfo->nexo > 0) {
            ret = 0;
          } else if (ainfo->Q > 0 && arma_missvals(ainfo)) {
            ret = 0;
          }
      }
    }

#if ARMA_DEBUG
    fprintf(stderr, "prefer_hr_init? %s\n", ret? "yes" : "no");
#endif

    return ret;
}

/* estimate an ARIMA (0,d,0) x (0,D,0) model via OLS */

static int arima_by_ls (const double **Z, const DATAINFO *pdinfo,
                  arma_info *ainfo, MODEL *pmod)
{
    gretl_matrix *X;
    gretl_matrix *b, *u, *V;
    double x, s2;
    int i, t, k = ainfo->dX->cols;
    int err = 0;

    if (ainfo->ifc) {
      /* the constant will not have been included in ainfo->dX */
      X = gretl_matrix_alloc(ainfo->T, k + 1);
      if (X == NULL) {
          return E_ALLOC;
      }
      for (i=0; i<=k; i++) {
          for (t=0; t<ainfo->T; t++) {
            if (i == 0) {
                gretl_matrix_set(X, t, i, 1.0);
            } else {
                x = gretl_matrix_get(ainfo->dX, t, i-1);
                gretl_matrix_set(X, t, i, x);
            }
          }
      }
      k++;
    } else {
      X = ainfo->dX;
    }

    b = gretl_column_vector_alloc(k);
    u = gretl_column_vector_alloc(ainfo->T);
    V = gretl_matrix_alloc(k, k);

    if (b == NULL || u == NULL || V == NULL) {
      err = E_ALLOC;
    } else {
      gretl_vector y;

      y.rows = ainfo->T;
      y.cols = 1;
      y.val = ainfo->y + ainfo->t1;
      y.t1 = ainfo->t1;
      y.t2 = ainfo->t2;

      err = gretl_matrix_ols(&y, X, b, V, u, &s2);
    }

    if (!err) {
      pmod->ncoeff = k;
      pmod->full_n = pdinfo->n;
      err = gretl_model_allocate_storage(pmod);
    }
    
    if (!err) {
      for (i=0; i<k; i++) {
          pmod->coeff[i] = b->val[i];
      }
      for (t=0; t<ainfo->T; t++) {
          pmod->uhat[t + ainfo->t1] = u->val[t];
      }     
      err = gretl_model_write_vcv(pmod, V, -1);
    }

    if (!err) {
      pmod->ybar = gretl_mean(ainfo->t1, ainfo->t2, ainfo->y);
      pmod->sdy = gretl_stddev(ainfo->t1, ainfo->t2, ainfo->y);
      pmod->nobs = ainfo->T;
    }
    
    gretl_matrix_free(b);
    gretl_matrix_free(u);
    gretl_matrix_free(V);

    if (X != ainfo->dX) {
      gretl_matrix_free(X);
    }

    return err;
}

static int arma_via_OLS (arma_info *ainfo, const double *coeff, 
                   const double **Z, const DATAINFO *pdinfo,
                   MODEL *pmod)
{
    int err = 0;

    ainfo->flags |= ARMA_LS;

    if (arma_xdiff(ainfo)) {
      err = arima_by_ls(Z, pdinfo, ainfo, pmod);
    } else {
      err = arma_by_ls(coeff, Z, pdinfo, ainfo, pmod);
    }

    if (!err) {
      ArmaFlags f = (arma_exact_ml(ainfo))? ARMA_OLS : ARMA_LS;

      pmod->t1 = ainfo->t1;
      pmod->t2 = ainfo->t2;
      pmod->full_n = pdinfo->n;
      write_arma_model_stats(pmod, ainfo, Z, pdinfo);
      if (arma_exact_ml(ainfo)) {
          ls_criteria(pmod);
      } else {
          arma_model_add_roots(pmod, ainfo, pmod->coeff);
      }
      gretl_model_set_int(pmod, "arma_flags", f);
    }

    return err;
}

/* Set flag to indicate differencing of exogenous regressors, in the
   case of an ARIMAX model using native exact ML -- unless this is
   forbidden by OPT_Y (--y-diff-only).  Note that we don't do this
   when we're using conditional ML (BHHH).
*/

static void maybe_set_xdiff_flag (arma_info *ainfo, gretlopt opt)
{
    if (arma_exact_ml(ainfo) &&
      (ainfo->d > 0 || ainfo->D > 0) &&
      ainfo->nexo > 0 && !(opt & OPT_Y)) {
      ainfo->pflags |= ARMA_XDIFF;
    }
}

/* Set flag to allow NAs within the sample range for an
   ARMA model using native exact ML. 
*/

static void maybe_allow_missvals (arma_info *ainfo)
{
    if (arma_exact_ml(ainfo)) {
      ainfo->pflags |= ARMA_NAOK;
    }
}

static int check_arma_options (gretlopt opt)
{
    int err;

    /* you can't specify LBFGS with conditional ML */
    err = incompatible_options(opt, OPT_C | OPT_L);

    if (!err) {
      /* nor --save-ehat with conditional ML */
      err = incompatible_options(opt, OPT_E | OPT_C);
    }

    if (!err) {
      /* nor --save-ehat with X-12-ARIMA */
      err = incompatible_options(opt, OPT_E | OPT_X);
    }      

    return err;
}

MODEL arma_model (const int *list, const int *pqspec,
              const double **Z, const DATAINFO *pdinfo, 
              gretlopt opt, PRN *prn)
{
    double *coeff = NULL;
    MODEL armod;
    arma_info ainfo_s, *ainfo;
    int init_done = 0;
    int missv = 0, misst = 0;
    int err = 0;

    ainfo = &ainfo_s;
    arma_info_init(ainfo, opt, pqspec, pdinfo);
    ainfo->prn = set_up_verbose_printer(opt, prn);

    gretl_model_init(&armod);

    err = check_arma_options(opt);

    if (!err) {
      ainfo->alist = gretl_list_copy(list);
      if (ainfo->alist == NULL) {
          err = E_ALLOC;
      }
    } 

    if (!err) {
      err = arma_check_list(ainfo, Z, pdinfo, opt);
    }

    if (!err) {
      /* calculate maximum lag */
      maybe_set_xdiff_flag(ainfo, opt);
      calc_max_lag(ainfo);
    }

    if (!err) {
      /* adjust sample range if need be */
      maybe_allow_missvals(ainfo);
      err = arma_adjust_sample(ainfo, Z, pdinfo, &missv, &misst);
      if (err) {
          gretl_errmsg_sprintf(_("Missing value encountered for "
                           "variable %d, obs %d"), missv, misst);
      } else if (missv > 0) {
          set_arma_missvals(ainfo);
      }
    }

    if (!err) {
      /* allocate initial coefficient vector */
      coeff = malloc(ainfo->nc * sizeof *coeff);
      if (coeff == NULL) {
          err = E_ALLOC;
      }
    }

    if (!err) {
      /* organize the dependent variable */
      ainfo->y = (double *) Z[ainfo->yno];
      if (ainfo->d > 0 || ainfo->D > 0) {
          if (arma_missvals(ainfo)) {
            set_arima_levels(ainfo);
          } else if (getenv("ARIMA_LEVELS")) {
            /* for testing purposes */
            set_arima_levels(ainfo);
          } else {
            /* this replaces ainfo->y */
            err = arima_difference(ainfo, Z, pdinfo, 0);
          }
      } 
    }

    if (err) {
      goto bailout;
    }

    if (ainfo->p == 0 && ainfo->P == 0 &&
      ainfo->q == 0 && ainfo->Q == 0 &&
      arma_exact_ml(ainfo) && !arma_missvals(ainfo)) {
      /* pure "I" model, no NAs: OLS provides the MLE */
      err = arma_via_OLS(ainfo, NULL, Z, pdinfo, &armod);
      goto bailout;
    }

    /* initialize the coefficients: there are 3 possible methods */

    /* first pass: see if the user specified some values */
    err = user_arma_init(coeff, ainfo, &init_done);
    if (err) {
      goto bailout;
    }

    if (!arma_exact_ml(ainfo) && ainfo->q == 0 && ainfo->Q == 0) {
      /* for a pure AR model, the conditional MLE is least squares */
      const double *b = (init_done)? coeff : NULL;

      err = arma_via_OLS(ainfo, b, Z, pdinfo, &armod);
      goto bailout;
    }

    /* second pass: try Hannan-Rissanen init, if suitable */
    if (!init_done && prefer_hr_init(ainfo)) {
      hr_arma_init(coeff, Z, pdinfo, ainfo, &init_done);
    }

    /* third pass: estimate pure AR model by OLS or NLS */
    if (!err && !init_done) {
      err = ar_arma_init(coeff, Z, pdinfo, ainfo, &armod);
    }

    if (!err) {
      clear_model_xpx(&armod);
      if (arma_exact_ml(ainfo)) {
          kalman_arma(coeff, Z, pdinfo, ainfo, &armod, opt);
      } else {
          bhhh_arma(coeff, Z, pdinfo, ainfo, &armod, opt);
      }
    }

 bailout:

    if (err && !armod.errcode) {
      armod.errcode = err;
    }

    if (!armod.errcode) {
      gretl_model_smpl_init(&armod, pdinfo);
    }

    free(coeff);
    arma_info_cleanup(ainfo);

    /* cleanup in MA roots checker */
    bounds_checker_cleanup();

    if (ainfo->prn != prn) {
      close_down_verbose_printer(ainfo->prn);
    }

    return armod;
}

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