/* Double Exponential Smoothing */
/* (n periods ahead) */
new; cls;
let data[12,1]=
23
25
36
31
26
28
48
36
31
42
53
43
;
nahead=4;
t=seqa(1,1,rows(data)+nahead);

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




proc desf(x,alpha,nahead);
   local n,m1,m2,m,mp,i,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;
   m=2*m1-m2;
   t=seqa(0,1,nahead+1);
   mp=miss(zeros(n-1,1),0)|m[n]+(alpha/(1-alpha))*(m1[n]-m2[n])*t;
   m=m|miss(zeros(nahead,1),0);
   retp(m~mp);
endp;