/*  ***********************************************************************  */
/*  CHAPITRE05 - LES POLITIQUES MONETAIRES EUROPEENNES ET LA REGLE DE TALOR  */
/*  ***********************************************************************  */

libname exo 'Z:\Econometrie appliquee\donnees';

ods pdf file="Z:\Econometrie appliquee\Resultats\chapitre05.pdf";
title;

*  ------------------------------- ;
*  Intitulé des différentes séries ;
*  ------------------------------- ;
*
tc_fr = taux d'intérêt à court terme de la France
tc_dm = taux d'intérêt à court terme de l'Allemagne
tc_nl = taux d'intérêt à court terme des Pays-Bas
tc_es = taux d'intérêt à court terme de l'Espagne
tc_it = taux d'intérêt à court terme de l'Italie
tc_uk = taux d'intérêt à court terme du Royaume-Uni
pib_fr = PIB en volume de la France
pib_dm = PIB en volume de l'Allemagne
pib_nl	= PIB en volume des Pays-Bas
pib_es = PIB en volume de l'Espagne
pib_it	= PIB en volume de l'Italie
pib_uk	= PIB en volume du Royaume-Uni
cpi_fr	= Indice des prix à la consommation de la France
cpi_dm	= Indice des prix à la consommation de l'Allemagne
cpi_nl	= Indice des prix à la consommation des Pays-Bas
cpi_es	= Indice des prix à la consommation de l'Espagne
cpi_it	= Indice des prix à la consommation de l'Italie
cpi_uk	= Indice des prix à la consommation du Royaume-Uni
;

*  -------------------------------------------------- ;
*  Problème 5.1 : Evaluation par simulation           ;
*  -------------------------------------------------- ;

* Création de la variable TRIMESTRE : 1970:1 à 1998:3 ;
* --------------------------------------------------- ;
data chapit5;
  set exo.chapit05;
  trimestre = intnx('QTR','01jan1970'd, _n_-1);
  format trimestre ddmmyy.;
  t=_n_;
run;

* Point 1 : Construction des variables d'intérêt du modèle ;
* -------------------------------------------------------- ;
data chapit5;
  set chapit5;
  * Question 1a : Création de la variable PIBGA_xx (glissement annuel du PIB pour le pays xx ;
  pibga_fr = 100 * (pib_fr - lag4(pib_fr)) / lag4(pib_fr);
  pibga_dm = 100 * (pib_dm - lag4(pib_dm)) / lag4(pib_dm);
  pibga_nl = 100 * (pib_nl - lag4(pib_nl)) / lag4(pib_nl);
  pibga_es = 100 * (pib_es - lag4(pib_es)) / lag4(pib_es);
  pibga_it = 100 * (pib_it - lag4(pib_it)) / lag4(pib_it);
  pibga_uk = 100 * (pib_uk - lag4(pib_uk)) / lag4(pib_uk);
  * Question 1b : Création de la variable CPIGA_xx (glissement annuel de l'indice des prix pour le pays xx ;
  cpiga_fr = 100 * (cpi_fr - lag4(cpi_fr)) / lag4(cpi_fr);
  cpiga_dm = 100 * (cpi_dm - lag4(cpi_dm)) / lag4(cpi_dm);
  cpiga_nl = 100 * (cpi_nl - lag4(cpi_nl)) / lag4(cpi_nl);
  cpiga_es = 100 * (cpi_es - lag4(cpi_es)) / lag4(cpi_es);
  cpiga_it = 100 * (cpi_it - lag4(cpi_it)) / lag4(cpi_it);
  cpiga_uk = 100 * (cpi_uk - lag4(cpi_uk)) / lag4(cpi_uk);
  * Question 1c : Ecart à l'inflation cible pour le pays xx ;
  ecinf_fr = cpiga_fr - 2;
  ecinf_dm = cpiga_dm - 2;
  ecinf_nl = cpiga_nl - 2;
  ecinf_es = cpiga_es - 2;
  ecinf_it = cpiga_it - 2;
  ecinf_uk = cpiga_uk - 2;
run;

* Question 1d : Application de la méthode de filtrage de Hodrick & Prescott pour les pays xx ;
proc expand data=chapit5 out=chapit5;
  convert pib_fr = hp_fr / TRANSFORMIN=(HP_T 1600);
  convert pib_dm = hp_dm / TRANSFORMIN=(HP_T 1600);
  convert pib_nl = hp_nl / TRANSFORMIN=(HP_T 1600);
  convert pib_es = hp_es / TRANSFORMIN=(HP_T 1600);
  convert pib_it = hp_it / TRANSFORMIN=(HP_T 1600);
  convert pib_uk = hp_uk / TRANSFORMIN=(HP_T 1600);
  id trimestre;
run;

* Glissement annuel du PIB potentiel pour le pays xx;
data chapit5;
  set chapit5;
  hpga_fr = 100 * (hp_fr - lag4(hp_fr)) / lag4(hp_fr);
  hpga_dm = 100 * (hp_dm - lag4(hp_dm)) / lag4(hp_dm);
  hpga_nl = 100 * (hp_nl - lag4(hp_nl)) / lag4(hp_nl);
  hpga_es = 100 * (hp_es - lag4(hp_es)) / lag4(hp_es);
  hpga_it = 100 * (hp_it - lag4(hp_it)) / lag4(hp_it);
  hpga_uk = 100 * (hp_uk - lag4(hp_uk)) / lag4(hp_uk);

  gap_fr = 100 * (pib_fr - hp_fr) / hp_fr;
  gap_dm = 100 * (pib_dm - hp_dm) / hp_dm;
  gap_nl = 100 * (pib_nl - hp_nl) / hp_nl;
  gap_es = 100 * (pib_es - hp_es) / hp_es;
  gap_it = 100 * (pib_it - hp_it) / hp_it;
  gap_uk = 100 * (pib_uk - hp_uk) / hp_uk;
run;

* Représentation graphique des séries suivantes :
     - PIB et PIB potentiel, 
     - Croissance et croissance potentielle,
     - Inflation et Output GAP ; 

goption reset=global;
title height=2 "PIB et PIB potentiel de l'Allemagne";
        legend1 frame
        across=1
	    mode=protect
	    position=(top left)
        offset=(3 cm, -1.5 cm); 
axis1 label=none order=(350 to 800 by 50) width=1 value=(h=1); 
axis2 label=none order=('01jan1970'd to '01jul1999'd by 365) width=1 value=(h=1);
 
proc gplot data=chapit5;
  symbol1 value=none i=join color=black;
  symbol2 value=none i=join color=red;
  plot (pib_dm hp_dm)*trimestre / overlay legend=legend1 haxis=axis2 vaxis=axis1 ;
  format trimestre year2.;
run;
quit;

goption reset=global;
title height=2 "Croissance et crooissance potentielle de l'Allemagne";
        legend1 frame
        across=1
	    mode=protect
	    position=(top left)
        offset=(3 cm, -1.5 cm); 
axis1 label=none order=(-4 to 16 by 4) width=1 value=(h=1); 
axis2 label=none order=('01jan1970'd to '01jul1999'd by 365) width=1 value=(h=1);
 
proc gplot data=chapit5;
  symbol1 value=none i=join color=black;
  symbol2 value=none i=join color=red;
  plot (hpga_dm pibga_dm)*trimestre / overlay legend=legend1 haxis=axis2 vaxis=axis1 vref=0;
  format trimestre year2.;
run;
quit;


goption reset=global;
title height=2 "Inflation et Output GAP de l'Allemagne";
        legend1 frame
        across=1
	    mode=protect
	    position=(top left)
        offset=(12 cm, -1 cm); 
axis1 label=none order=(-4 to 8 by 2) width=1 value=(h=1); 
axis2 label=none order=('01jan1970'd to '01jul1999'd by 365) width=1 value=(h=1);
 
proc gplot data=chapit5;
  symbol1 value=none i=join color=black;
  symbol2 value=none i=join color=red;
  plot (gap_dm cpiga_dm)*trimestre / overlay legend=legend1 haxis=axis2 vaxis=axis1 vref=0;
  format trimestre year2.;
run;
quit;

* Point 2 : Calcul des séries de taux de Taylor et de taux neutre ;
* --------------------------------------------------------------- ;
data chapit5;
  set chapit5;
  * Taux de Taylor;
  ts_fr = hpga_fr + cpiga_fr + 0.5*ecinf_fr + 0.5*gap_fr;
  ts_dm = hpga_dm + cpiga_dm + 0.5*ecinf_dm + 0.5*gap_dm;
  ts_nl = hpga_nl + cpiga_nl + 0.5*ecinf_nl + 0.5*gap_nl;
  ts_es = hpga_es + cpiga_es + 0.5*ecinf_es + 0.5*gap_es;
  ts_it = hpga_it + cpiga_it + 0.5*ecinf_it + 0.5*gap_it;
  ts_uk = hpga_uk + cpiga_uk + 0.5*ecinf_uk + 0.5*gap_uk;
  * Taux neutre;
  tn_fr = hpga_fr + cpiga_fr;
  tn_dm = hpga_dm + cpiga_dm;
  tn_nl = hpga_nl + cpiga_nl;
  tn_es = hpga_es + cpiga_es;
  tn_it = hpga_it + cpiga_it;
  tn_it = hpga_it + cpiga_it;
  tn_uk = hpga_uk + cpiga_uk;
run;

goption reset=global;
title1 height=2 "Taux courts, taux neutres et taux de Taylor";
title2 height=2 "             de l'Allemagne                ";
        legend1 frame
        across=1
	    mode=protect
	    position=(top left)
        offset=(10 cm, -1 cm); 
axis1 label=none order=(0 to 15 by 2.5) width=1 value=(h=1); 
axis2 label=none order=('01jan1970'd to '01jul1999'd by 365) width=1 value=(h=1);
 
proc gplot data=chapit5;
  symbol1 value=none i=join color=black;
  symbol2 value=none i=join color=red;
  symbol3 value=none i=join color=blue;
  plot (tc_dm ts_dm tn_dm)*trimestre / overlay legend=legend1 haxis=axis2 vaxis=axis1 vref=0;
  format trimestre year2.;
run;
quit;


goption reset=global;
title1 height=2 "Taux courts, taux neutres et taux de Taylor";
title2 height=2 "             de la France                  ";
        legend1 frame
        across=1
	    mode=protect
	    position=(top left)
        offset=(15 cm, -1 cm); 
axis1 label=none order=(0 to 25 by 5) width=1 value=(h=1); 
axis2 label=none order=('01jan1970'd to '01jul1999'd by 365) width=1 value=(h=1);
 
proc gplot data=chapit5;
  symbol1 value=none i=join color=black;
  symbol2 value=none i=join color=red;
  symbol3 value=none i=join color=blue;
  plot (tc_fr ts_fr tn_fr)*trimestre / overlay legend=legend1 haxis=axis2 vaxis=axis1 vref=0;
  format trimestre year2.;
run;
quit;

goption reset=global;
title1 height=2 "Taux courts, taux neutres et taux de Taylor";
title2 height=2 "             du Royaume-Unis               ";
        legend1 frame
        across=1
	    mode=protect
	    position=(top left)
        offset=(15 cm, -1 cm); 
axis1 label=none order=(0 to 40 by 5) width=1 value=(h=1); 
axis2 label=none order=('01jan1970'd to '01jul1999'd by 365) width=1 value=(h=1);
 
proc gplot data=chapit5;
  symbol1 value=none i=join color=black;
  symbol2 value=none i=join color=red;
  symbol3 value=none i=join color=blue;
  plot (tc_uk ts_uk tn_uk)*trimestre / overlay legend=legend1 haxis=axis2 vaxis=axis1 vref=0;
  format trimestre year2.;
run;
quit;

* Point 3 : Calcul de l'indicateur de précision du modèle explicatif des taux courts ;
* ---------------------------------------------------------------------------------- ;
* Précision de la règle de Taylor simulée avec lambda1=lambda2=0 (RMSE sur 12 trimestres);
* ---------------------------------------------------------------------------------------;
data chapit5;
  set chapit5;
  * Différence entre taux court et taux neutre;
  ecn_fr = tc_fr - tn_fr;
  ec2n_fr=ecn_fr**2;
  ecn_dm = tc_dm - tn_dm;
  ec2n_dm=ecn_dm**2;
  ecn_nl = tc_nl - tn_nl;
  ec2n_nl=ecn_nl**2;
  ecn_es = tc_es - tn_es;
  ec2n_es=ecn_es**2;
  ecn_it = tc_it - tn_it;
  ec2n_it=ecn_it**2;
  ecn_uk = tc_uk - tn_uk;
  ec2n_uk=ecn_uk**2;
run;

 proc expand data=chapit5 out=chapit5 method=none; 
      id trimestre; 
	  * France;
      convert ec2n_fr = ec2n_fr1  / transformout=(lead 1); 
      convert ec2n_fr = ec2n_fr2  / transformout=(lead 2); 
      convert ec2n_fr = ec2n_fr3  / transformout=(lead 3); 
      convert ec2n_fr = ec2n_fr4  / transformout=(lead 4); 
      convert ec2n_fr = ec2n_fr5  / transformout=(lead 5); 
      convert ec2n_fr = ec2n_fr6  / transformout=(lead 6); 
      convert ec2n_fr = ec2n_fr7  / transformout=(lead 7); 
      convert ec2n_fr = ec2n_fr8  / transformout=(lead 8); 
      convert ec2n_fr = ec2n_fr9  / transformout=(lead 9); 
      convert ec2n_fr = ec2n_fr10 / transformout=(lead 10); 
      convert ec2n_fr = ec2n_fr11 / transformout=(lead 11); 
      convert ec2n_fr = ec2n_fr12 / transformout=(lead 12); 
	  * Allemagne;
      convert ec2n_dm = ec2n_dm1  / transformout=(lead 1); 
      convert ec2n_dm = ec2n_dm2  / transformout=(lead 2); 
      convert ec2n_dm = ec2n_dm3  / transformout=(lead 3); 
      convert ec2n_dm = ec2n_dm4  / transformout=(lead 4); 
      convert ec2n_dm = ec2n_dm5  / transformout=(lead 5); 
      convert ec2n_dm = ec2n_dm6  / transformout=(lead 6); 
      convert ec2n_dm = ec2n_dm7  / transformout=(lead 7); 
      convert ec2n_dm = ec2n_dm8  / transformout=(lead 8); 
      convert ec2n_dm = ec2n_dm9  / transformout=(lead 9); 
      convert ec2n_dm = ec2n_dm10 / transformout=(lead 10); 
      convert ec2n_dm = ec2n_dm11 / transformout=(lead 11); 
      convert ec2n_dm = ec2n_dm12 / transformout=(lead 12); 
	  * Pays-Bas;
      convert ec2n_nl = ec2n_nl1  / transformout=(lead 1); 
      convert ec2n_nl = ec2n_nl2  / transformout=(lead 2); 
      convert ec2n_nl = ec2n_nl3  / transformout=(lead 3); 
      convert ec2n_nl = ec2n_nl4  / transformout=(lead 4); 
      convert ec2n_nl = ec2n_nl5  / transformout=(lead 5); 
      convert ec2n_nl = ec2n_nl6  / transformout=(lead 6); 
      convert ec2n_nl = ec2n_nl7  / transformout=(lead 7); 
      convert ec2n_nl = ec2n_nl8  / transformout=(lead 8); 
      convert ec2n_nl = ec2n_nl9  / transformout=(lead 9); 
      convert ec2n_nl = ec2n_nl10 / transformout=(lead 10); 
      convert ec2n_nl = ec2n_nl11 / transformout=(lead 11); 
      convert ec2n_nl = ec2n_nl12 / transformout=(lead 12); 
	  * Espagne;
      convert ec2n_es = ec2n_es1  / transformout=(lead 1); 
      convert ec2n_es = ec2n_es2  / transformout=(lead 2); 
      convert ec2n_es = ec2n_es3  / transformout=(lead 3); 
      convert ec2n_es = ec2n_es4  / transformout=(lead 4); 
      convert ec2n_es = ec2n_es5  / transformout=(lead 5); 
      convert ec2n_es = ec2n_es6  / transformout=(lead 6); 
      convert ec2n_es = ec2n_es7  / transformout=(lead 7); 
      convert ec2n_es = ec2n_es8  / transformout=(lead 8); 
      convert ec2n_es = ec2n_es9  / transformout=(lead 9); 
      convert ec2n_es = ec2n_es10 / transformout=(lead 10); 
      convert ec2n_es = ec2n_es11 / transformout=(lead 11); 
      convert ec2n_es = ec2n_es12 / transformout=(lead 12); 
	  * Italie;
      convert ec2n_it = ec2n_it1  / transformout=(lead 1); 
      convert ec2n_it = ec2n_it2  / transformout=(lead 2); 
      convert ec2n_it = ec2n_it3  / transformout=(lead 3); 
      convert ec2n_it = ec2n_it4  / transformout=(lead 4); 
      convert ec2n_it = ec2n_it5  / transformout=(lead 5); 
      convert ec2n_it = ec2n_it6  / transformout=(lead 6); 
      convert ec2n_it = ec2n_it7  / transformout=(lead 7); 
      convert ec2n_it = ec2n_it8  / transformout=(lead 8); 
      convert ec2n_it = ec2n_it9  / transformout=(lead 9); 
      convert ec2n_it = ec2n_it10 / transformout=(lead 10); 
      convert ec2n_it = ec2n_it11 / transformout=(lead 11); 
      convert ec2n_it = ec2n_it12 / transformout=(lead 12); 
	  * Royaume-Uni;
      convert ec2n_uk = ec2n_uk1  / transformout=(lead 1); 
      convert ec2n_uk = ec2n_uk2  / transformout=(lead 2); 
      convert ec2n_uk = ec2n_uk3  / transformout=(lead 3); 
      convert ec2n_uk = ec2n_uk4  / transformout=(lead 4); 
      convert ec2n_uk = ec2n_uk5  / transformout=(lead 5); 
      convert ec2n_uk = ec2n_uk6  / transformout=(lead 6); 
      convert ec2n_uk = ec2n_uk7  / transformout=(lead 7); 
      convert ec2n_uk = ec2n_uk8  / transformout=(lead 8); 
      convert ec2n_uk = ec2n_uk9  / transformout=(lead 9); 
      convert ec2n_uk = ec2n_uk10 / transformout=(lead 10); 
      convert ec2n_uk = ec2n_uk11 / transformout=(lead 11); 
      convert ec2n_uk = ec2n_uk12 / transformout=(lead 12); 
run;

data chapit5;
  set chapit5;
  mean_ec2n_fr = mean(of ec2n_fr1--ec2n_fr12);
  mean_ec2n_dm = mean(of ec2n_dm1--ec2n_dm12);
  mean_ec2n_nl = mean(of ec2n_nl1--ec2n_nl12);
  mean_ec2n_it = mean(of ec2n_it1--ec2n_it12);
  mean_ec2n_es = mean(of ec2n_es1--ec2n_es12);
  mean_ec2n_uk = mean(of ec2n_uk1--ec2n_uk12);
  rmse_fr = lag12(sqrt(mean_ec2n_fr));
  rmse_dm = lag12(sqrt(mean_ec2n_dm));
  rmse_nl = lag12(sqrt(mean_ec2n_nl));
  rmse_it = lag12(sqrt(mean_ec2n_it));
  rmse_es = lag12(sqrt(mean_ec2n_es));
  rmse_uk = lag12(sqrt(mean_ec2n_uk)); 
run; 

data chapit5;  
  set chapit5; 
  drop ec2n_fr1--ec2n_uk12 mean_ec2n_fr--mean_ec2n_uk;
run;

goption reset=global;
title height=2 "Précision de la règle de Taylor simulée";
        legend1 frame
        across=1
	    mode=protect
	    position=(top left)
        offset=(15 cm, -1 cm); 
axis1 label=none order=(0 to 18 by 2) width=1 value=(h=1); 
axis2 label=none order=('01jan1973'd to '01jul1999'd by 365) width=1 value=(h=1);
 
proc gplot data=chapit5;
  symbol1 value=none i=join color=black;
  symbol2 value=none i=join color=red;
  symbol3 value=none i=join color=blue;
  symbol4 value=none i=join color=orange;
  symbol5 value=none i=join color=green;
  symbol6 value=none i=join color=cyan;
  plot (rmse_fr rmse_dm rmse_nl rmse_it rmse_es rmse_uk)*trimestre / overlay legend=legend1 haxis=axis2 vaxis=axis1 vref=0;
  format trimestre year2.;
run;
quit;

* Précision de la règle de Taylor simulée avec lambda1=lambda2=0.5 (RMSE sur 12 trimestres);
* -----------------------------------------------------------------------------------------;
data chapit5;
  set chapit5;
  * Différence entre taux court et taux de Taylor;
  er_fr = tc_fr - ts_fr;
  er2_fr=er_fr**2;
  er_dm = tc_dm - ts_dm;
  er2_dm=er_dm**2;
  er_nl = tc_nl - ts_nl;
  er2_nl=er_nl**2;
  er_es = tc_es - ts_es;
  er2_es=er_es**2;
  er_it = tc_it - ts_it;
  er2_it=er_it**2;
  er_uk = tc_uk - ts_uk;
  er2_uk=er_uk**2;
run;

 proc expand data=chapit5 out=chapit5 method=none; 
      id trimestre; 
	  * France;
      convert er2_fr = er2_fr1  / transformout=(lead 1); 
      convert er2_fr = er2_fr2  / transformout=(lead 2); 
      convert er2_fr = er2_fr3  / transformout=(lead 3); 
      convert er2_fr = er2_fr4  / transformout=(lead 4); 
      convert er2_fr = er2_fr5  / transformout=(lead 5); 
      convert er2_fr = er2_fr6  / transformout=(lead 6); 
      convert er2_fr = er2_fr7  / transformout=(lead 7); 
      convert er2_fr = er2_fr8  / transformout=(lead 8); 
      convert er2_fr = er2_fr9  / transformout=(lead 9); 
      convert er2_fr = er2_fr10 / transformout=(lead 10); 
      convert er2_fr = er2_fr11 / transformout=(lead 11); 
      convert er2_fr = er2_fr12 / transformout=(lead 12); 
	  * Allemagne;
      convert er2_dm = er2_dm1  / transformout=(lead 1); 
      convert er2_dm = er2_dm2  / transformout=(lead 2); 
      convert er2_dm = er2_dm3  / transformout=(lead 3); 
      convert er2_dm = er2_dm4  / transformout=(lead 4); 
      convert er2_dm = er2_dm5  / transformout=(lead 5); 
      convert er2_dm = er2_dm6  / transformout=(lead 6); 
      convert er2_dm = er2_dm7  / transformout=(lead 7); 
      convert er2_dm = er2_dm8  / transformout=(lead 8); 
      convert er2_dm = er2_dm9  / transformout=(lead 9); 
      convert er2_dm = er2_dm10 / transformout=(lead 10); 
      convert er2_dm = er2_dm11 / transformout=(lead 11); 
      convert er2_dm = er2_dm12 / transformout=(lead 12); 
	  * Pays-Bas;
      convert er2_nl = er2_nl1  / transformout=(lead 1); 
      convert er2_nl = er2_nl2  / transformout=(lead 2); 
      convert er2_nl = er2_nl3  / transformout=(lead 3); 
      convert er2_nl = er2_nl4  / transformout=(lead 4); 
      convert er2_nl = er2_nl5  / transformout=(lead 5); 
      convert er2_nl = er2_nl6  / transformout=(lead 6); 
      convert er2_nl = er2_nl7  / transformout=(lead 7); 
      convert er2_nl = er2_nl8  / transformout=(lead 8); 
      convert er2_nl = er2_nl9  / transformout=(lead 9); 
      convert er2_nl = er2_nl10 / transformout=(lead 10); 
      convert er2_nl = er2_nl11 / transformout=(lead 11); 
      convert er2_nl = er2_nl12 / transformout=(lead 12); 
	  * Espagne;
      convert er2_es = er2_es1  / transformout=(lead 1); 
      convert er2_es = er2_es2  / transformout=(lead 2); 
      convert er2_es = er2_es3  / transformout=(lead 3); 
      convert er2_es = er2_es4  / transformout=(lead 4); 
      convert er2_es = er2_es5  / transformout=(lead 5); 
      convert er2_es = er2_es6  / transformout=(lead 6); 
      convert er2_es = er2_es7  / transformout=(lead 7); 
      convert er2_es = er2_es8  / transformout=(lead 8); 
      convert er2_es = er2_es9  / transformout=(lead 9); 
      convert er2_es = er2_es10 / transformout=(lead 10); 
      convert er2_es = er2_es11 / transformout=(lead 11); 
      convert er2_es = er2_es12 / transformout=(lead 12); 
	  * Italie;
      convert er2_it = er2_it1  / transformout=(lead 1); 
      convert er2_it = er2_it2  / transformout=(lead 2); 
      convert er2_it = er2_it3  / transformout=(lead 3); 
      convert er2_it = er2_it4  / transformout=(lead 4); 
      convert er2_it = er2_it5  / transformout=(lead 5); 
      convert er2_it = er2_it6  / transformout=(lead 6); 
      convert er2_it = er2_it7  / transformout=(lead 7); 
      convert er2_it = er2_it8  / transformout=(lead 8); 
      convert er2_it = er2_it9  / transformout=(lead 9); 
      convert er2_it = er2_it10 / transformout=(lead 10); 
      convert er2_it = er2_it11 / transformout=(lead 11); 
      convert er2_it = er2_it12 / transformout=(lead 12); 
	  * Royaume-Uni;
      convert er2_uk = er2_uk1  / transformout=(lead 1); 
      convert er2_uk = er2_uk2  / transformout=(lead 2); 
      convert er2_uk = er2_uk3  / transformout=(lead 3); 
      convert er2_uk = er2_uk4  / transformout=(lead 4); 
      convert er2_uk = er2_uk5  / transformout=(lead 5); 
      convert er2_uk = er2_uk6  / transformout=(lead 6); 
      convert er2_uk = er2_uk7  / transformout=(lead 7); 
      convert er2_uk = er2_uk8  / transformout=(lead 8); 
      convert er2_uk = er2_uk9  / transformout=(lead 9); 
      convert er2_uk = er2_uk10 / transformout=(lead 10); 
      convert er2_uk = er2_uk11 / transformout=(lead 11); 
      convert er2_uk = er2_uk12 / transformout=(lead 12); 
run;

data chapit5;
  set chapit5;
  mean_er2_fr = mean(of er2_fr1--er2_fr12);
  mean_er2_dm = mean(of er2_dm1--er2_dm12);
  mean_er2_nl = mean(of er2_nl1--er2_nl12);
  mean_er2_it = mean(of er2_it1--er2_it12);
  mean_er2_es = mean(of er2_es1--er2_es12);
  mean_er2_uk = mean(of er2_uk1--er2_uk12);
  rmsee_fr = lag12(sqrt(mean_er2_fr));
  rmsee_dm = lag12(sqrt(mean_er2_dm));
  rmsee_nl = lag12(sqrt(mean_er2_nl));
  rmsee_it = lag12(sqrt(mean_er2_it));
  rmsee_es = lag12(sqrt(mean_er2_es));
  rmsee_uk = lag12(sqrt(mean_er2_uk)); 
run; 

data chapit5;  
  set chapit5; 
  drop er2_fr1--er2_uk12 mean_er2_fr--mean_er2_uk;
run;

goption reset=global;
title height=2 "Precision de la regle de Taylor simulee";
        legend1 frame
        across=1
	    mode=protect
	    position=(top left)
        offset=(15 cm, -1 cm); 
axis1 label=none order=(0 to 30 by 5) width=1 value=(h=1); 
axis2 label=none order=('01jan1973'd to '01jul1999'd by 365) width=1 value=(h=1);
 
proc gplot data=chapit5;
  symbol1 value=none i=join color=black;
  symbol2 value=none i=join color=red;
  symbol3 value=none i=join color=blue;
  symbol4 value=none i=join color=orange;
  symbol5 value=none i=join color=green;
  symbol6 value=none i=join color=cyan;
  plot (rmsee_fr rmsee_dm rmsee_nl rmsee_it rmsee_es rmsee_uk)*trimestre / overlay legend=legend1 haxis=axis2 vaxis=axis1 vref=0;
  format trimestre year2.;
run;
quit;

*  -------------------------------------------------------------------- ;
*  Problème 5.2 : Evaluation pas estimation et tests sur longue période ;
*  -------------------------------------------------------------------- ;

* Point 1 : Estimation du modèle contraint pour chaque pays;
* ---------------------------------------------------------;
proc reg data=chapit5;
  model ecn_fr = ecinf_fr gap_fr;
  output out=chapit5 p=ecs_fr ;
  title "Estimation pour la France";
run;

proc reg data=chapit5;
  model ecn_dm = ecinf_dm gap_dm;
  output out=chapit5 p=ecs_dm ;
  title "Estimation pour l'Allemagne";
run;

proc reg data=chapit5;
  model ecn_nl = ecinf_nl gap_nl;
  output out=chapit5 p=ecs_nl ;
  title "Estimation pour les Pays-Bas";
run;

proc reg data=chapit5;
  model ecn_it = ecinf_it gap_it;
  output out=chapit5 p=ecs_it ;
  title "Estimation pour l'Italie";
run;

proc reg data=chapit5;
  model ecn_es = ecinf_es gap_es;
  output out=chapit5 p=ecs_es ;
  title "Estimation pour l'Espagne";
run;

proc reg data=chapit5;
  model ecn_uk = ecinf_uk gap_uk;
  output out=chapit5 p=ecs_uk;
  title "Estimation pour le Royaume-Uni";
run;
quit;

data chapit5;
   set chapit5;
   te_fr = ecs_fr +tn_fr;
   te_dm = ecs_dm +tn_dm;
   te_nl = ecs_nl +tn_nl;
   te_it = ecs_it +tn_it;
   te_es = ecs_es +tn_es;
   te_uk = ecs_uk +tn_uk;
 run;

goption reset=global;
title1 height=2 "Taux courts, taux de taylor et taux estimés";
title2 height=2 "Allemagne";
        legend1 frame
        across=1
	    mode=protect
	    position=(top left)
        offset=(10 cm, -1 cm); 
axis1 label=none order=(0 to 15 by 2.5) width=1 value=(h=1); 
axis2 label=none order=('01jan1970'd to '01jul1999'd by 365) width=1 value=(h=1);
 
proc gplot data=chapit5;
  symbol1 value=none i=join color=black;
  symbol2 value=none i=join color=red;
  symbol3 value=none i=join color=blue;
  plot (tc_dm ts_dm te_dm)*trimestre / overlay legend=legend1 haxis=axis2 vaxis=axis1 vref=0;
  format trimestre year2.;
run;
quit;

goption reset=global;
title1 height=2 "Taux courts, taux de taylor et taux estimés";
title2 height=2 "France";
        legend1 frame
        across=1
	    mode=protect
	    position=(top left)
        offset=(13 cm, -1 cm); 
axis1 label=none order=(0 to 25 by 5) width=1 value=(h=1); 
axis2 label=none order=('01jan1970'd to '01jul1999'd by 365) width=1 value=(h=1);
 
proc gplot data=chapit5;
  symbol1 value=none i=join color=black;
  symbol2 value=none i=join color=red;
  symbol3 value=none i=join color=blue;
  plot (tc_fr ts_fr te_fr)*trimestre / overlay legend=legend1 haxis=axis2 vaxis=axis1 vref=0;
  format trimestre year2.;
run;
quit;


goption reset=global;
title1 height=2 "Taux courts, taux de taylor et taux estimés";
title2 height=2 "France";
        legend1 frame
        across=1
	    mode=protect
	    position=(top left)
        offset=(13 cm, -1 cm); 
axis1 label=none order=(0 to 40 by 5) width=1 value=(h=1); 
axis2 label=none order=('01jan1970'd to '01jul1999'd by 365) width=1 value=(h=1);
 
proc gplot data=chapit5;
  symbol1 value=none i=join color=black;
  symbol2 value=none i=join color=red;
  symbol3 value=none i=join color=blue;
  plot (tc_uk ts_uk te_uk)*trimestre / overlay legend=legend1 haxis=axis2 vaxis=axis1 vref=0;
  format trimestre year2.;
run;
quit;

* Point 4 : Test sur les paramètres lambda1 et lambda2;
* ----------------------------------------------------;
proc reg data=chapit5;
  model ecn_fr = ecinf_fr gap_fr;
  test1 : test ecinf_fr=0.5 ;
  test2 : test gap_fr=0.5;
  test3 : test ecinf_fr=gap_fr=0.5;
  title "Tests pour la France";
run;
quit;

proc reg data=chapit5;
  model ecn_dm = ecinf_dm gap_dm;
  test1 : test ecinf_dm=0.5 ;
  test2 : test gap_dm=0.5;
  test3 : test ecinf_dm=gap_dm=0.5;
  title "Tests pour l'Allemagne";
run;
quit;

proc reg data=chapit5;
  model ecn_nl = ecinf_nl gap_nl;
  test1 : test ecinf_nl=0.5 ;
  test2 : test gap_nl=0.5;
  test3 : test ecinf_nl=gap_nl=0.5;
  title "Tests pour les Pays-Bas";
run;
quit;

proc reg data=chapit5;
  model ecn_it = ecinf_it gap_it;
  test1 : test ecinf_it=0.5 ;
  test2 : test gap_it=0.5;
  test3 : test ecinf_it=gap_it=0.5;
  title "Tests pour l'Italie";
run;
quit;

proc reg data=chapit5;
  model ecn_es = ecinf_es gap_es;
  test1 : test ecinf_es=0.5 ;
  test2 : test gap_es=0.5;
  test3 : test ecinf_es=gap_es=0.5;
  title "Tests pour l'Espagne";
run;
quit;

proc reg data=chapit5;
  model ecn_uk = ecinf_uk gap_uk;
  test1 : test ecinf_uk=0.5 ;
  test2 : test gap_uk=0.5;
  test3 : test ecinf_uk=gap_uk=0.5;
  title "Tests pour le Royaume-Uni";
run;
quit;

*  -------------------------------------- ;
*  Problème 5.3 : Analyse de la stabilité ;
*  -------------------------------------- ;

* Point 1 : Estimation par sous-période;
* -------------------------------------; 
data chapit5;
  set chapit5;
 /* if '01jan70'd <= trimestre < '01jan80'd then periode1=1; else periode1=0;
  if '01jan80'd <= trimestre < '01jan90'd then periode2=1; else periode2=0;
  if '01jan88'd <= trimestre <= '01jul98'd then periode3=1;else periode3=0;
  if '01jan90'd <= trimestre <= '01jul98'd then periode4=1;else periode4=0; */

  if '01jan70'd <= trimestre < '01jan80'd then periode="periode1";
    else if '01jan80'd <= trimestre < '01jan90'd then periode="periode2";
    else if '01jan90'd <= trimestre <= '01jul98'd then periode="periode3";

  if '01jan90'd <= trimestre <= '01jul98'd then periode4=1;else periode4=0; 
  format trimestre ddmmyy8.;
run;

proc freq data=chapit5;
  table periode periode4;
run;

* Estimation et test sur la période 1 (1970 à 1979);
* ------------------------------------------------; 
proc sort data=chapit5; by periode; run;

proc reg data=chapit5;
  model ecn_fr = ecinf_fr gap_fr;
  by periode;
  test1 : test ecinf_fr=0.5 ;
  test2 : test gap_fr=0.5;
  test3 : test ecinf_fr=gap_fr=0.5;
  title "Tests pour la France";
run;
quit;

proc reg data=chapit5;
  model ecn_dm = ecinf_dm gap_dm;
  by periode;
  test1 : test ecinf_dm=0.5 ;
  test2 : test gap_dm=0.5;
  test3 : test ecinf_dm=gap_dm=0.5;
  title "Tests pour l'Allemagne";
run;
quit;

proc reg data=chapit5;
  model ecn_nl = ecinf_nl gap_nl;
  by periode;
  test1 : test ecinf_nl=0.5 ;
  test2 : test gap_nl=0.5;
  test3 : test ecinf_nl=gap_nl=0.5;
  title "Tests pour les Pays-Bas";
run;
quit;

proc reg data=chapit5;
  model ecn_it = ecinf_it gap_it;
  by periode;
  test1 : test ecinf_it=0.5 ;
  test2 : test gap_it=0.5;
  test3 : test ecinf_it=gap_it=0.5;
  title "Tests pour l'Italie";
run;
quit;

proc reg data=chapit5;
  model ecn_es = ecinf_es gap_es;
  by periode;
  test1 : test ecinf_es=0.5 ;
  test2 : test gap_es=0.5;
  test3 : test ecinf_es=gap_es=0.5;
  title "Tests pour l'Espagne";
run;
quit;

proc reg data=chapit5;
  model ecn_uk = ecinf_uk gap_uk;
  by periode;
  test1 : test ecinf_uk=0.5 ;
  test2 : test gap_uk=0.5;
  test3 : test ecinf_uk=gap_uk=0.5;
  title "Tests pour le Royaume-Uni";
run;
quit;


* Point 2 : Test de stabilité de CUSUM;
* ------------------------------------; 
* La France;
* ---------;
proc autoreg data=chapit5;
  model ecn_fr = ecinf_fr gap_fr /reset;
  output out=res_fr recres=recur cusum=c1 cusumlb=lb cusumub=ub;
run;

goption reset=global;
title1 height=2 "Test de stabilite des parametres";
title2 height=2 "France";
        legend1 frame
        across=1
	    mode=protect
	    position=(top left)
        offset=(13 cm, -1 cm); 
axis1 label=none order=(-40 to 80 by 20) width=1 value=(h=1); 
axis2 label=none order=('01jan1973'd to '01jul1999'd by 365) width=1 value=(h=1);
 
proc gplot data=res_fr;
  symbol1 value=none i=join color=black;
  symbol2 value=none i=join color=red;
  symbol3 value=none i=join color=red;
  plot (c1 lb ub)*trimestre / overlay legend=legend1 haxis=axis2 vaxis=axis1 ;
  format trimestre year2.;
run;
quit;

* L'Allemagne;
* -----------;
proc autoreg data=chapit5;
  model ecn_dm = ecinf_dm gap_dm /reset;
  output out=res_dm recres=recur cusum=c1 cusumlb=lb cusumub=ub;
run;

goption reset=global;
title1 height=2 "Test de stabilite des parametres";
title2 height=2 "Allemagne";
        legend1 frame
        across=1
	    mode=protect
	    position=(top left)
        offset=(13 cm, -1 cm); 
axis1 label=none order=(-32 to 80 by 16) width=1 value=(h=1); 
axis2 label=none order=('01jan1973'd to '01jul1999'd by 365) width=1 value=(h=1);
 
proc gplot data=res_dm;
  symbol1 value=none i=join color=black;
  symbol2 value=none i=join color=red;
  symbol3 value=none i=join color=red;
  plot (c1 lb ub)*trimestre / overlay legend=legend1 haxis=axis2 vaxis=axis1 ;
  format trimestre year2.;
run;
quit;

* Les Pays-Bas;
* ------------;
proc autoreg data=chapit5;
  model ecn_nl = ecinf_nl gap_nl /reset;
  output out=res_nl recres=recur cusum=c1 cusumlb=lb cusumub=ub;
run;

goption reset=global;
title1 height=2 "Test de stabilite des parametres";
title2 height=2 "Pays-Bas";
        legend1 frame
        across=1
	    mode=protect
	    position=(top left)
        offset=(13 cm, -1 cm); 
axis1 label=none order=(-32 to 32 by 8) width=1 value=(h=1); 
axis2 label=none order=('01jul1978'd to '01jul1999'd by 365) width=1 value=(h=1);
 
proc gplot data=res_nl;
  symbol1 value=none i=join color=black;
  symbol2 value=none i=join color=red;
  symbol3 value=none i=join color=red;
  plot (c1 lb ub)*trimestre / overlay legend=legend1 haxis=axis2 vaxis=axis1 ;
  format trimestre year2.;
run;
quit;

* L'Espagne;
* ---------;
proc autoreg data=chapit5;
  model ecn_es = ecinf_es gap_es /reset;
  output out=res_es recres=recur cusum=c1 cusumlb=lb cusumub=ub;
run;

goption reset=global;
title1 height=2 "Test de stabilite des parametres";
title2 height=2 "Espagne";
        legend1 frame
        across=1
	    mode=protect
	    position=(top left)
        offset=(13 cm, -1 cm); 
axis1 label=none order=(-32 to 40 by 8) width=1 value=(h=1); 
axis2 label=none order=('01oct1973'd to '01jul1999'd by 365) width=1 value=(h=1);
 
proc gplot data=res_es;
  symbol1 value=none i=join color=black;
  symbol2 value=none i=join color=red;
  symbol3 value=none i=join color=red;
  plot (c1 lb ub)*trimestre / overlay legend=legend1 haxis=axis2 vaxis=axis1 ;
  format trimestre year2.;
run;
quit;

* L'Italie;
* --------;
proc autoreg data=chapit5;
  model ecn_it = ecinf_it gap_it /reset;
  output out=res_it recres=recur cusum=c1 cusumlb=lb cusumub=ub;
run;

goption reset=global;
title1 height=2 "Test de stabilite des parametres";
title2 height=2 "Italie";
        legend1 frame
        across=1
	    mode=protect
	    position=(top left)
        offset=(13 cm, -1 cm); 
axis1 label=none order=(-40 to 100 by 20) width=1 value=(h=1); 
axis2 label=none order=('01jul1973'd to '01jul1999'd by 365) width=1 value=(h=1);
 
proc gplot data=res_it;
  symbol1 value=none i=join color=black;
  symbol2 value=none i=join color=red;
  symbol3 value=none i=join color=red;
  plot (c1 lb ub)*trimestre / overlay legend=legend1 haxis=axis2 vaxis=axis1 ;
  format trimestre year2.;
run;
quit;

* Le Royaume-Uni;
* --------------;
proc autoreg data=chapit5;
  model ecn_uk = ecinf_uk gap_uk /reset;
  output out=res_uk recres=recur cusum=c1 cusumlb=lb cusumub=ub;
run;

goption reset=global;
title1 height=2 "Test de stabilite des parametres";
title2 height=2 "Royaume-Uni";
        legend1 frame
        across=1
	    mode=protect
	    position=(top left)
        offset=(13 cm, -1 cm); 
axis1 label=none order=(-32 to 32 by 8) width=1 value=(h=1); 
axis2 label=none order=('01oct1975'd to '01jul1999'd by 365) width=1 value=(h=1);
 
proc gplot data=res_uk;
  symbol1 value=none i=join color=black;
  symbol2 value=none i=join color=red;
  symbol3 value=none i=join color=red;
  plot (c1 lb ub)*trimestre / overlay legend=legend1 haxis=axis2 vaxis=axis1 ;
  format trimestre year2.;
run;
quit;

ods pdf close;