/* This program graphs the ACF and PACF of an MA(1) process.
   For invertibility, -1 < theta1 < 1. */

data a;

    theta1= -0.8; /* You can change the value of theta1*/

    do lag = 1 to 30;
    if lag = 1 then phijj=-theta1/(1+theta1**2);
	else if lag = 2 then phijj=-(theta1**2)/(1+theta1**2+theta1**4);
    else phijj=((-(theta1**lag))*(1-theta1**2))/(1-theta1**(2*(lag+1)));
    if lag = 1 then rho=-theta1/(1+theta1**2);
    else rho=0;
      
   output;
   end;
run;

symbol interpol=needle
       cv=blue
	   ci=black
	   value=dot
	   height=1
	   width=1;


proc gplot data=a;
    title1 'Theoretical ACF for MA(1) Process';
    title2 'with theta1 = -0.8';
    plot rho*lag;
run;
    title1 'Theoretical PACF for MA(1) Process';
    title2 'with theta1 = -0.8';
    plot phijj*lag;
run;