/* Brown's one-Prameter quadratric */
new; cls;
let data[12,1]=
23
25
36
31
26
28
48
36
31
42
53
43
;
nahead=10;
t=seqa(1,1,rows(data)+nahead);

library pgraph;
graphset;
_pltype=6;
_plegctl=1;
_plegstr="actual\000predicted";
title("QUAD");
alpha=0.2;
xy(t,(data|miss(zeros(nahead,1),0))~quad(data,alpha,nahead));




proc quad(x,alpha,nahead);
   local n,m1,m2,m3,m,mp,i,b,c,t;
   n=rows(x);
   m1=zeros(n,1);
   m1[1]=x[1];
   i=2;
   do while i<=n;
      m1[i]=alpha*x[i-1]+(1-alpha)*m1[i-1]; 
      i=i+1;
   endo;
   m2=zeros(n,1);
   m2[1]=m1[1];
   i=2;
   do while i<=n;
      m2[i]=alpha*m1[i-1]+(1-alpha)*m2[i-1]; 
      i=i+1;
   endo;
   m3=zeros(n,1);
   m3[1]=m2[1];
   i=2;
   do while i<=n;
      m3[i]=alpha*m2[i-1]+(1-alpha)*m3[i-1]; 
      i=i+1;
   endo;
   m=3*m1-3*m2+m3;
   b=alpha^2/(2*(1-alpha)^2)*((6-5*alpha)*m1[n]-(10-8*alpha)*m2[n]+(4-3*alpha)*m3[n]);
   c=alpha^2/((1-alpha)^2)*(m1[n]-2*m2[n]+m3[n]);
   t=seqa(0,1,nahead+1);
   mp=miss(zeros(n-1,1),0)|m[n]+0.5*b*t+c*t^2;
   m=m|miss(zeros(nahead,1),0);
   retp(m~mp);
endp;