/* This program generates some cointegrated series under various settings */

/* Case 1: no drift in x and y, no constant in C.I. relationship,
           no trend in C.I. relationship.                           */

options pagesize=60 linesize=74 nodate;
goptions reset=all device=win target=winprtm rotate=landscape;

data case1;

  alpha = 0; mu1 = 0;
  rhox = 0.5; ex1 = 0;
  rhoy = 0.5; ey1 = 0;

  do i = -50 to 150;
     emu = rannor(3);
     ux = rannor(2);
     uy = rannor(5);
     mu = alpha + mu1 + emu;
     ex = rhox*ex1 + ux;
     ey = rhoy*ey1 + uy;
     x = mu + ex + 0.5*ey;
     y = 1.0*mu + ey + 0.5*ex;
     obs = i;
     if i > 0 then output;
     mu1 = mu;
     ex1 = ex;
     ey1 = ey;
     end;
  keep obs x y;

proc print data = case1;
  title1 'Cointegrated Time Series';
  title2 'Case 1: No drift in Series, no constant in C.I. relationship';
  title3 '        no trend in C.I. relationship';

proc gplot data=case1;
  symbol1 c=black v=y h=.8;
  symbol2 c=black v=x h=.8;
  title1 'Cointegrated Time Series';
  title2 'Case 1: No drift in Series, no constant in C.I. relationship';
  title3 '        no trend in C.I. relationship';
  axis1 order=(0 to 150 by 10)
  label=(f=duplex 'Obs');
  axis2 order=(-5 to 25 by 5)
  label=(f=duplex 'C.I. Time Series');
  plot y*obs = 1 x*obs = 2 / overlay haxis=axis1 vaxis=axis2;

run;

data case2;

  alpha = 0; mu1 = 0;
  rhox = 0.5; ex1 = 0;
  rhoy = 0.5; ey1 = 0;

  do i = -50 to 150;
     emu = rannor(3);
     ux = rannor(2);
     uy = rannor(5);
     mu = alpha + mu1 + emu;
     ex = rhox*ex1 + ux;
     ey = rhoy*ey1 + uy;
     x = mu + ex + 0.5*ey;
     y = 10 + 1.0*mu + ey + 0.5*ex;
     obs = i;
     if i > 0 then output;
     mu1 = mu;
     ex1 = ex;
     ey1 = ey;
     end;
  keep obs x y;

proc print data = case2;
  title1 'Cointegrated Time Series';
  title2 'Case 2: No drift in Series, constant in C.I. relationship';
  title3 '        no trend in C.I. relationship';

proc gplot data=case2;
  symbol1 c=black v=y h=.8;
  symbol2 c=black v=x h=.8;
  title1 'Cointegrated Time Series';
  title2 'Case 2: No drift in Series, constant in C.I. relationship';
  title3 '        no trend in C.I. relationship';
  axis1 order=(0 to 150 by 10)
  label=(f=duplex 'Obs');
  axis2 order=(-3 to 33 by 3)
  label=(f=duplex 'C.I. Time Series');
  plot y*obs = 1 x*obs = 2 / overlay haxis=axis1 vaxis=axis2;

run;

data case3a;

  alpha = 0.2; mu1 = 0;
  rhox = 0.5; ex1 = 0;
  rhoy = 0.5; ey1 = 0;

  do i = -50 to 150;
     emu = rannor(3);
     ux = rannor(2);
     uy = rannor(5);
     mu = alpha + mu1 + emu;
     ex = rhox*ex1 + ux;
     ey = rhoy*ey1 + uy;
     x =  mu + ex + 0.5*ey;
     y = 1.0*mu + ey + 0.5*ex;
     obs = i;
     if i > 0 then output;
     mu1 = mu;
     ex1 = ex;
     ey1 = ey;
     end;
  keep obs x y;

proc print data = case3a;
  title1 'Cointegrated Time Series';
  title2 'Case 3a: Drift in Series, no constant in C.I. relationship';
  title3 '        no trend in C.I. relationship';

proc gplot data=case3a;
  symbol1 c=black v=y h=.8;
  symbol2 c=black v=x h=.8;
  title1 'Cointegrated Time Series';
  title2 'Case 3a: Drift in Series, no constant in C.I. relationship';
  title3 '        no trend in C.I. relationship';
  axis1 order=(0 to 150 by 10)
  label=(f=duplex 'Obs');
  axis2 order=(0 to 70 by 10)
  label=(f=duplex 'C.I. Time Series');
  plot y*obs = 1 x*obs = 2 / overlay haxis=axis1 vaxis=axis2;

run;

data case3b;

  alpha = 0.2; mu1 = 0;
  rhox = 0.5; ex1 = 0;
  rhoy = 0.5; ey1 = 0;

  do i = -50 to 150;
     emu = rannor(3);
     ux = rannor(2);
     uy = rannor(5);
     mu = alpha + mu1 + emu;
     ex = rhox*ex1 + ux;
     ey = rhoy*ey1 + uy;
     x =  mu + ex + 0.5*ey;
     y = 10 + 1.0*mu + ey + 0.5*ex;
     obs = i;
     if i > 0 then output;
     mu1 = mu;
     ex1 = ex;
     ey1 = ey;
     end;
  keep obs x y;

proc print data = case3b;
  title1 'Cointegrated Time Series';
  title2 'Case 3b: Drift in Series, constant in C.I. relationship';
  title3 '        no trend in C.I. relationship';

proc gplot data=case3b;
  symbol1 c=black v=y h=.8;
  symbol2 c=black v=x h=.8;
  title1 'Cointegrated Time Series';
  title2 'Case 3b: Drift in Series, constant in C.I. relationship';
  title3 '        no trend in C.I. relationship';
  axis1 order=(0 to 150 by 10)
  label=(f=duplex 'Obs');
  axis2 order=(0 to 70 by 10)
  label=(f=duplex 'C.I. Time Series');
  plot y*obs = 1 x*obs = 2 / overlay haxis=axis1 vaxis=axis2;

run;

data case4a;

  alpha = 0.2; mu1 = 0;
  rhox = 0.5; ex1 = 0;
  rhoy = 0.5; ey1 = 0;

  do i = -50 to 150;
     emu = rannor(3);
     ux = rannor(2);
     uy = rannor(5);
     mu = alpha + mu1 + emu;
     ex = rhox*ex1 + ux;
     ey = rhoy*ey1 + uy;
     x =  mu + ex + 0.5*ey;
     y = 1.0*mu + 0.2*i + ey + 0.5*ex;
     obs = i;
     if i > 0 then output;
     mu1 = mu;
     ex1 = ex;
     ey1 = ey;
     end;
  keep obs x y;

proc print data = case4a;
  title1 'Cointegrated Time Series';
  title2 'Case 4a: Drift in Series, no constant in C.I. relationship';
  title3 '         trend in C.I. relationship';

proc gplot data=case4a;
  symbol1 c=black v=y h=.8;
  symbol2 c=black v=x h=.8;
  title1 'Cointegrated Time Series';
  title2 'Case 4a: Drift in Series, no constant in C.I. relationship';
  title3 '         trend in C.I. relationship';
  axis1 order=(0 to 150 by 10)
  label=(f=duplex 'Obs');
  axis2 order=(0 to 120 by 10)
  label=(f=duplex 'C.I. Time Series');
  plot y*obs = 1 x*obs = 2 / overlay haxis=axis1 vaxis=axis2;

run;

data case4b;

  alpha = 0.2; mu1 = 0;
  rhox = 0.5; ex1 = 0;
  rhoy = 0.5; ey1 = 0;

  do i = -50 to 150;
     emu = rannor(3);
     ux = rannor(2);
     uy = rannor(5);
     mu = alpha + mu1 + emu;
     ex = rhox*ex1 + ux;
     ey = rhoy*ey1 + uy;
     x =  mu + ex + 0.5*ey;
     y = 10 + 1.0*mu + 0.2*i + ey + 0.5*ex;
     obs = i;
     if i > 0 then output;
     mu1 = mu;
     ex1 = ex;
     ey1 = ey;
     end;
  keep obs x y;

proc print data = case4b;
  title1 'Cointegrated Time Series';
  title2 'Case 4b: Drift in Series, constant in C.I. relationship';
  title3 '         trend in C.I. relationship';

proc gplot data=case4b;
  symbol1 c=black v=y h=.8;
  symbol2 c=black v=x h=.8;
  title1 'Cointegrated Time Series';
  title2 'Case 4b: Drift in Series, constant in C.I. relationship';
  title3 '         trend in C.I. relationship';
  axis1 order=(0 to 150 by 10)
  label=(f=duplex 'Obs');
  axis2 order=(0 to 120 by 10)
  label=(f=duplex 'C.I. Time Series');
  plot y*obs = 1 x*obs = 2 / overlay haxis=axis1 vaxis=axis2;

run;