/* This program generates some monte carlo data for use in the forecasting                                                              
   class.  The first series is an invertible MA(1) process with
   theta1 = -0.9.  The second series is an invertible MA(1) process
   with theta1 = 0.9.  */                                      
                                            
options pagesize=60 linesize=74 nodate;                                                                                                 
goptions device=win                                                                                                                     
gsfname=plot                                                                                                                            
rotate=landscape                                                                                                                        
gsfmode=append                                                                                                                          
target=hpljs3;                                                                                                                          
*border;                                                                                                                                
                                                                                                                                        
/* This segment of the program generates the invertible MA(1) model                                                                     
   with theta1 = -0.9  */                                                                                                                 
                                                               
data mc1;                                                                                                                           
                                                                                                                                        
  u1=0; a=-0.9;                                                                                                                         
  do t = 0 to 100;                                                                                                                      
   u=rannor(145923);                                                                                                                    
   y = 50 + u - a*u1;                                                                                                                   
   if t > 0 then output;
   u1=u;
  end;
                                                                                                                                        
proc gplot data=mc1;                                                                                                                    
  symbol v=dot c=black i=join h=.8;                                                                                                     
  title1 'Monte Carlo MA(1) data with theta(1) = -0.9';                                                                                    
  title2 'X=Time Y=MA(1) Series';                                                                                                       
  axis1 order=(0 to 100 by 10)                                                                                                          
  label=(f=duplex 'Obs');                                                                                                               
  axis2 order=(40 to 60 by 5)                                                                                                          
  label=(f=duplex 'MA(1) Series');                                                                                                      
  plot y*t / haxis=axis1 vaxis=axis2;

  run;

title ' Monte Carlo MA(1) data with theta(1) = -0.9';
  proc arima data=mc1;
    identify var=y;

    run;

/* This segment of the program generates the invertible MA(1) model                                                                     
   with theta1 = 0.9  */

data mc2;                                                                                                                           
                                                                                                                                        
  u=0; a=0.9;                                                                                                                         
  do t = 0 to 100;                                                                                                                      
   u1=u;                                                                                                                                
   u=rannor(189763);                                                                                                                    
   y = 50 + u - a*u1;                                                                                                                   
   if t > 0 then output;                                                                                                              
  end;
                                                                                                                                        
proc gplot data=mc2;                                                                                                                    
  symbol v=dot c=black i=join h=.8;                                                                                                     
  title1 'Monte Carlo MA(1) data with theta(1) = 0.9';                                                                                    
  title2 'X=Time Y=MA(1) Series';                                                                                                       
  axis1 order=(0 to 100 by 10)                                                                                                          
  label=(f=duplex 'Obs');                                                                                                               
  axis2 order=(40 to 60 by 5)                                                                                                          
  label=(f=duplex 'MA(1) Series');                                                                                                      
  plot y*t / haxis=axis1 vaxis=axis2;

  run;

 title 'Monte Carlo MA(1) data with theta(1) = 0.9';

 proc arima data=mc2;
   identify var = y;

   run;