arima-model.c

时间序列工具

    swap=iterate[0];
    for (i=0;i<poles;i++)
      iterate[i]=iterate[i+1];
    iterate[poles]=swap;
  }

  for (i=0;i<=poles;i++)
    free(iterate[i]);
  free(iterate);
  for (i=0;i<dim;i++)
    free(myrand[i]);
  free(myrand);
}

int main(int argc,char **argv)
{
  char stdi=0;
  double *pm;
  long i,j,iter,hj,realiter=0;
  unsigned int size,is,id;
  FILE *file;
  double **mat,**inverse,*vec,**coeff,**diff,**hseries;
  double **oldcoeff,*diffcoeff=NULL;
  double hdiff,**xdiff=NULL,avpm;
  double loglikelihood,aic,alldiff;
  
  if (scan_help(argc,argv))
    show_options(argv[0]);
  
  scan_options(argc,argv);
#ifndef OMIT_WHAT_I_DO
  if (verbosity&VER_INPUT)
    what_i_do(argv[0],WID_STR);
#endif

  infile=search_datafile(argc,argv,NULL,verbosity);
  if (infile == NULL)
    stdi=1;

  if (outfile == NULL) {
    if (!stdi) {
      check_alloc(outfile=(char*)calloc(strlen(infile)+5,(size_t)1));
      strcpy(outfile,infile);
      strcat(outfile,".ari");
    }
    else {
      check_alloc(outfile=(char*)calloc((size_t)10,(size_t)1));
      strcpy(outfile,"stdin.ari");
    }
  }
  if (!stdo)
    test_outfile(outfile);

  if (column == NULL)
    series=(double**)get_multi_series(infile,&length,exclude,&dim,"",dimset,
				      verbosity);
  else
    series=(double**)get_multi_series(infile,&length,exclude,&dim,column,
				      dimset,verbosity);

  check_alloc(my_average=(double*)malloc(sizeof(double)*dim));

  for (i=0;i<ipoles;i++)
    make_difference();

  for (i=0;i<dim;i++)
    series[i] += ipoles;
  length -= ipoles;

  set_averages_to_zero();

  if (poles >= length) {
    fprintf(stderr,"It makes no sense to have more poles than data! Exiting\n");
    exit(AR_MODEL_TOO_MANY_POLES);
  }
  if (arimaset) {
    if ((arpoles >= length) || (mapoles >= length)) {
      fprintf(stderr,"It makes no sense to have more poles than data! Exiting\n");
      exit(AR_MODEL_TOO_MANY_POLES);
    }
  }
 
  ardim=poles*dim;
  aindex=make_ar_index();

  check_alloc(vec=(double*)malloc(sizeof(double)*ardim));
  check_alloc(mat=(double**)malloc(sizeof(double*)*ardim));
  for (i=0;i<ardim;i++)
    check_alloc(mat[i]=(double*)malloc(sizeof(double)*ardim));

  check_alloc(coeff=(double**)malloc(sizeof(double*)*dim));
  inverse=build_matrix(mat,ardim);
  for (i=0;i<dim;i++) {
    build_vector(vec,ardim,i);
    coeff[i]=multiply_matrix_vector(inverse,vec,ardim);
  }

  check_alloc(diff=(double**)malloc(sizeof(double*)*dim));
  for (i=0;i<dim;i++)
    check_alloc(diff[i]=(double*)malloc(sizeof(double)*length));

  pm=make_residuals(diff,coeff,ardim);

  free(vec);
  for (i=0;i<ardim;i++) {
    free(mat[i]);
    free(inverse[i]);
  }
  free(mat);
  free(inverse);
  size=ardim;
  
  if (arimaset) {
    offset=poles;
    for (i=0;i<2;i++)
      free(aindex[i]);
    free(aindex);

    for (i=0;i<dim;i++)
      free(coeff[i]);
    free(coeff);
    check_alloc(xdiff=(double**)malloc(sizeof(double*)*ITER));
    for (i=0;i<ITER;i++)
      check_alloc(xdiff[i]=(double*)malloc(sizeof(double)*dim));

    armadim=(arpoles+mapoles)*dim;
    aindex=make_arima_index(arpoles,mapoles);
    size=armadim;

    check_alloc(hseries=(double**)malloc(sizeof(double*)*2*dim));
    for (i=0;i<dim;i++) {
      check_alloc(hseries[i]=(double*)malloc(sizeof(double)*length));
      check_alloc(hseries[i+dim]=(double*)malloc(sizeof(double)*length));
      for (j=0;j<length;j++) {
	hseries[i][j]=series[i][j];
	hseries[i+dim][j]=diff[i][j];
      }
    }

    for (i=0;i<dim;i++)
      free(series[i]-ipoles);
    free(series);

    series=hseries;

    check_alloc(oldcoeff=(double**)malloc(sizeof(double*)*dim));
    for (i=0;i<dim;i++) {
      check_alloc(oldcoeff[i]=(double*)malloc(sizeof(double)*armadim));
      for (j=0;j<armadim;j++)
	oldcoeff[i][j]=0.0;
    }
    check_alloc(diffcoeff=(double*)malloc(sizeof(double)*ITER));

    for (iter=1;iter<=ITER;iter++) {
      check_alloc(vec=(double*)malloc(sizeof(double)*armadim));
      check_alloc(mat=(double**)malloc(sizeof(double*)*armadim));
      for (i=0;i<armadim;i++)
	check_alloc(mat[i]=(double*)malloc(sizeof(double)*armadim));

      check_alloc(coeff=(double**)malloc(sizeof(double*)*dim));

      poles=(arpoles > mapoles)? arpoles:mapoles;

      offset += poles;
      inverse=build_matrix(mat,armadim);

      for (i=0;i<dim;i++) {
	build_vector(vec,armadim,i);
	coeff[i]=multiply_matrix_vector(inverse,vec,armadim);
      }

      pm=make_residuals(diff,coeff,armadim);

      for (j=0;j<dim;j++) {
	hdiff=0.0;
	hj=j+dim;
	for (i=offset;i<length;i++)
	  hdiff += sqr(series[hj][i]-diff[j][i]);
	for (i=0;i<length;i++) {
	  series[hj][i]=diff[j][i];
	}
	xdiff[iter-1][j]=sqrt(hdiff/(double)(length-offset));
      }

      free(vec);
      for (i=0;i<armadim;i++) {
	free(mat[i]);
	free(inverse[i]);
      }
      free(mat);
      free(inverse);

      diffcoeff[iter-1]=0.0;
      for (i=0;i<dim;i++)
	for (j=0;j<dim;j++) {
	  diffcoeff[iter-1] += sqr(coeff[i][j]-oldcoeff[i][j]);
	  oldcoeff[i][j]=coeff[i][j];
	}
      diffcoeff[iter-1]=sqrt(diffcoeff[iter-1]/(double)armadim);
      alldiff=xdiff[iter-1][0];
      for (i=1;i<dim;i++)
	if (xdiff[iter-1][i] > alldiff)
	  alldiff=xdiff[iter-1][i];
      realiter=iter;
      if (alldiff < convergence)
	iter=ITER;
  
      if (iter < ITER) {
	for (i=0;i<dim;i++)
	  free(coeff[i]);
	free(coeff);
      }
    }
  }

  if (stdo) {
    if (arimaset) {
      printf("#convergence of residuals in arima fit\n");
      for (i=0;i<realiter;i++) {
	printf("#iteration %ld ",i+1);
	for (j=0;j<dim;j++)
	  printf("%e ",xdiff[i][j]);
	printf("%e",diffcoeff[i]);
	printf("\n");
      }
    }
    avpm=pm[0]*pm[0];
    loglikelihood= -log(pm[0]);
    for (i=1;i<dim;i++) {
      avpm += pm[i]*pm[i];
      loglikelihood -= log(pm[i]);
    }
    loglikelihood *= ((double)length);
    loglikelihood += -((double)length)*
      ((1.0+log(2.*M_PI))*dim)/2.0;
    avpm=sqrt(avpm/dim);
    printf("#average forcast error= %e\n",avpm);
    printf("#individual forecast errors: ");
     for (i=0;i<dim;i++)
      printf("%e ",pm[i]);
    printf("\n");
    if (arimaset)
      aic=2.0*(arpoles+mapoles)-2.0*loglikelihood;
    else
      aic=2.0*poles-2.0*loglikelihood;
    printf("#Log-Likelihood= %e\t AIC= %e\n",loglikelihood,aic);
    for (i=0;i<size;i++) {
      id=aindex[0][i];
      is=aindex[1][i];
      if (id < dim)
	printf("#x_%u(n-%u) ",id+1,is);
      else
	printf("#e_%u(n-%u) ",id+1-dim,is);
      for (j=0;j<dim;j++)
	printf("%e ",coeff[j][i]);
      printf("\n");
    }
    if (!run_model || (verbosity&VER_USR1)) {
      for (i=poles;i<length;i++) {
	if (run_model)
	  printf("#");
	for (j=0;j<dim;j++)
	  if (verbosity&VER_USR2)
	    printf("%e %e ",series[j][i]+my_average[j],diff[j][i]);
	  else
	    printf("%e ",diff[j][i]);
	printf("\n");
      }
    }
    if (run_model && (ilength > 0)) {
      if (!arimaset)
	iterate_model(coeff,pm,diff,NULL);
      else 
	iterate_arima_model(coeff,pm,diff,NULL);
    }
  }
  else {
    file=fopen(outfile,"w");
    if (verbosity&VER_INPUT)
      fprintf(stderr,"Opened %s for output\n",outfile);
    if (arimaset) {
      fprintf(file,"#convergence of residuals in arima fit\n");
      for (i=0;i<realiter;i++) {
	fprintf(file,"#iteration %ld ",i+1);
	for (j=0;j<dim;j++)
	  fprintf(file,"%e ",xdiff[i][j]);
	fprintf(file,"%e",diffcoeff[i]);
	fprintf(file,"\n");
      }
    }
    avpm=pm[0]*pm[0];
    loglikelihood= -log(pm[0]);
    for (i=1;i<dim;i++) {
      avpm += pm[i]*pm[i];
      loglikelihood -= log(pm[i]);
    }
    loglikelihood *= ((double)length);
    loglikelihood += -((double)length)*
      ((1.0+log(2.*M_PI))*dim)/2.0;
    avpm=sqrt(avpm/dim);
    fprintf(file,"#average forcast error= %e\n",avpm);
    fprintf(file,"#individual forecast errors: ");
    for (i=0;i<dim;i++)
      fprintf(file,"%e ",pm[i]);
    fprintf(file,"\n");
    if (arimaset)
      aic=2.0*(arpoles+mapoles)-2.0*loglikelihood;
    else
      aic=2.0*poles-2.0*loglikelihood;
    fprintf(file,"#Log-Likelihood= %e\t AIC= %e\n",loglikelihood,aic);
    for (i=0;i<size;i++) {
      id=aindex[0][i];
      is=aindex[1][i];
      if (id < dim)
	fprintf(file,"#x_%u(n-%u) ",id+1,is);
      else
	fprintf(file,"#e_%u(n-%u) ",id+1-dim,is);
      for (j=0;j<dim;j++)
	fprintf(file,"%e ",coeff[j][i]);
      fprintf(file,"\n");
    }
    if (!run_model || (verbosity&VER_USR1)) {
      for (i=poles;i<length;i++) {
	if (run_model)
	  fprintf(file,"#");
	for (j=0;j<dim;j++)
	  if (verbosity&VER_USR2)
	    fprintf(file,"%e %e ",series[j][i]+my_average[j],diff[j][i]);
	  else
	    fprintf(file,"%e ",diff[j][i]);
	fprintf(file,"\n");
      }
    }
    if (run_model && (ilength > 0)) {
      if (!arimaset)
	iterate_model(coeff,pm,diff,file);
      else
	iterate_arima_model(coeff,pm,diff,file);
    }
    fclose(file);
  }
  if (outfile != NULL)
    free(outfile);
  if (infile != NULL)
    free(infile);
  for (i=0;i<dim;i++) {
    free(coeff[i]);
    free(diff[i]);
    free(series[i]);
    if (arimaset)
      free(series[i+dim]);
  }
  free(coeff);
  free(diff);
  free(series);

  free(pm);

  return 0;
}