data oil;
input year prod;
cards;
1880	30
1890	77
1900	149
1905	215
1910	328
1915	432
1920	689
1925	1069
1930	1412
1935	1655
1940	2150
1945	2595
1950	3803
1955	5626
1960	7674
1962	8882
1964	10310
1966	12016
1968	14104
1970	16690
1972	18584
1974	20389
1976	20188
1978	21922
1980	21732
1982	19403
1984	19608
;

proc gplot data=oil;
title "Production fonction de l annee";
symbol1 color=red interpol=join value=dot;
plot prod*year;
run;
data oil1;
   set oil;
     t=year-1880;
proc nlin data=oil1;
title "Regression nonlinéaire"; 
  parameters a=3.4 b=0.08 c=-0.00017;
  model prod=exp(a+b*t+c*t*t);
    der.a=exp(a+b*t+c*t*t); 
    der.b=t*exp(a+b*t+c*t*t);
    der.c=t*t*exp(a+b*t+c*t*t);
  output out=sortie1 r=residus;
     run;

  proc gplot data=sortie1;
  title "Residus fonction de temps";
symbol1 color=red interpol=join value=dot;
 plot residus*t; run;
 
 proc arima data=sortie1;
 title1 "Série chronologique";
 title2 "Etape identification";
 identify var=residus stationarity=(dickey=6); run;
 identify var=residus(1) stationarity=(dickey=6); run;
identify var=residus(1,1) stationarity=(dickey=6); run;
title2 "Etape estimation";
   estimate p=1 plot;
   estimate q=1 plot;
   estimate p=1 q=1 plot;
 run;
 quit;