/*  This program demonstrates the classical decomposition of a time series:
         Y = T + C + S + I where
         Y = time series to be described
         T = Trend
         C = Cycle
         S = Seasonal
         I = Irregular           */
     
/*  This segment of the program generates a Deterministic Trend. */

data mc1;

do t = 1 to 100;
  
tr = 100.0 + 4.0*t;

  output;

end;

keep tr t;

proc gplot data=mc1;
  symbol v=dot c=black i=join h=.8;
  title1 'Deterministic Trend Data';
  title2 'X=Time Y=Trend Series';
  axis1 order=(0 to 100 by 10)
  label=(f=duplex 'Time');
  axis2 order=(-100 to 700 by 100)
  label=(f=duplex 'Trend Series');
  plot tr*t / haxis=axis1 vaxis=axis2;

  run;

/*  This segment of the program generates a Deterministic Cycle. */

data mc2;

do t = 1 to 100;

c = 50*cos(3.1416*t/10);

 output;

end;

keep c t;

proc gplot data=mc2;
  symbol v=dot c=black i=join h=.8;
  title1 'Cycle with a=50, w = 2pi/20 (period = 20 months), theta = 0';
  title2 'X=Time Y=Cyclical Series';
  axis1 order=(0 to 100 by 10)
  label=(f=duplex 'Time');
  axis2 order=(-150 to 150 by 30)
  label=(f=duplex 'Cycle');
  plot c*t / haxis=axis1 vaxis=axis2;

  run;

/*  This segment of the program generates a Deterministic Seasonal.
    The Seasonal Effects add to one.  */

data seasonal;
  input mon s;
  datalines;
1 -50
2 -25
3 25
4 -25
5 -50
6 50
7 75
8 50
9 5
10 -25
11 -50
12 20
;

proc gplot data=seasonal;
  symbol v=dot c=black i=join h=.8;
  title1 'Seasonal Effects by Month';
  title2 'X=Time Y=Seasonal Effects';
  axis1 order=(1 to 12 by 1)
  label=(f=duplex 'Time');
  axis2 order=(-150 to 150 by 30)
  label=(f=duplex 'Seasonal Effects');
  plot s*mon / haxis=axis1 vaxis=axis2;

  run;

/* Setting up the seasonal effects and the seasonal dummy variables.  */

data mc3;

do t = 1 to 100;
    
  month = mod(t,12);

  if month = 0 then month = 12;

  if month = 1 then s = -50;
  if month = 2 then s = -25;
  if month = 3 then s = 25;
  if month = 4 then s = -25;
  if month = 5 then s = -50;
  if month = 6 then s = 50;
  if month = 7 then s = 75;
  if month = 8 then s = 50;
  if month = 9 then s = 5;
  if month = 10 then s = -25;
  if month = 11 then s = -50;
  if month = 12 then s = 20;

  if month = 2 then dum2 = 1; else dum2 = 0;
  if month = 3 then dum3 = 1; else dum3 = 0;
  if month = 4 then dum4 = 1; else dum4 = 0;
  if month = 5 then dum5 = 1; else dum5 = 0;
  if month = 6 then dum6 = 1; else dum6 = 0;
  if month = 7 then dum7 = 1; else dum7 = 0;
  if month = 8 then dum8 = 1; else dum8 = 0;
  if month = 9 then dum9 = 1; else dum9 = 0;
  if month = 10 then dum10 = 1; else dum10 = 0;
  if month = 11 then dum11 = 1; else dum11 = 0;
  if month = 12 then dum12 = 1; else dum12 = 0;
  
  output;

  end;

  run;

  title 'Seasonal Effects and Seasonal Dummy Variables';

  proc print data = mc3;

/*  This segment of the program generates the Irregular Component. */

data mc4;
 do t = 1 to 100;
 
  i = 10*rannor(t);

  output;
   
  end;

  run;

proc gplot data=mc4;
  symbol v=dot c=black i=join h=.8;
  title1 'Irregular Component';
  title2 'X=Time Y=Irregular Component';
  axis1 order=(0 to 100 by 10)
  label=(f=duplex 'Time');
  axis2 order=(-150 to 150 by 30)
  label=(f=duplex 'Irregular Component');
  plot i*t / haxis=axis1 vaxis=axis2;

  run;

  data combine;
     merge mc1 mc2 mc3 mc4;

  data combine;
     set combine;
     y1 = tr;
	 y2 = tr + c;
	 y3 = tr + c + s;
	 y4 = tr + c + s + i;
     y5 = y4/100;
     z = exp(y5); 
     logz = log(z); 
	 run;

proc gplot data=combine;
  symbol v=dot c=black i=join h=.8;
  title1 'Exponential Growth Data';
  title2 'X=Time Y=Exp Growth Data';
  axis1 order=(0 to 100 by 10)
  label=(f=duplex 'Time');
  axis2 order=(0 to 300 by 25)
  label=(f=duplex 'Exp Growth Data');
  plot z*t / haxis=axis1 vaxis=axis2;

  run;

proc gplot data=combine;
  symbol v=dot c=black i=join h=.8;
  title1 'Log Transform of Exponential Growth Data';
  title2 'X=Time Y=Logged Data';
  axis1 order=(0 to 100 by 10)
  label=(f=duplex 'Time');
  axis2 order=(0 to 6 by 1)
  label=(f=duplex 'Logged Data');
  plot logz*t / haxis=axis1 vaxis=axis2;

  run;