/*  This program generates Monte Carlo data for an ARIMA(0,1,1)
    model.  */

options pagesize=60 linesize=74 nodate;                                                                                                    
goptions device=win                                                                                                                        
gsfname=plot                                                                                                                               
rotate=landscape                                                                                                                           
gsfmode=append                                                                                                                             
target=hpljs3;                                                                                                                             
*border; 

data mc;
  y1 = 0.9; a1 = 0;
  do t = 0 to 100;
     a = rannor(14398);
     y = y1 + a - 0.7 * a1 + 0.2;
     if t > 0 then output;
     a1 = a;
     y1 = y;
     end;

proc gplot data=mc;                                                                                                                       
  symbol v=dot c=black i=join h=.8;                                                                                                        
  title1 'Monte Carlo IMA(1) data with theta(1) = -0.7';                                                                                    
  title2 'X=Time Y=IMA(1) Series';                                                                                                          
  axis1 order=(0 to 100 by 10)                                                                                                             
  label=(f=duplex 'Obs');                                                                                                                  
  axis2 order=(-5 to 30 by 5)                                                                                                              
  label=(f=duplex 'IMA(1) Series');                                                                                                         
  plot y*t / haxis=axis1 vaxis=axis2;

data mc;
  set mc;
  dy = y - lag1(y);

run;

title 'ACF and PACF for Nonstationary ARIMA(0,1,1) series';
proc arima data=mc;
  identify var = y;

  run;

title 'ACF and PACF for Differenced ARIMA(0,1,1) series';
proc arima data=mc;
  identify var = y(1);

  run;

proc gplot data=mc;                                                                                                                       
  symbol v=dot c=black i=join h=.8;                                                                                                        
  title1 'Differenced IMA(1) data with theta(1) = -0.7';                                                                                    
  title2 'X=Time Y=DY(1) Series';                                                                                                          
  axis1 order=(0 to 100 by 10)                                                                                                             
  label=(f=duplex 'Obs');                                                                                                                  
  axis2 order=(-10 to 10 by 5)                                                                                                              
  label=(f=duplex 'IMA(1) Series');                                                                                                         
  plot dy*t / haxis=axis1 vaxis=axis2;
                                                                                                                                          
  run;