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

library pgraph;
graphset;
_pltype=6;
_plegctl=1;
_plegstr="actual\000predicted\000n ahead";
title("Damped Trend Exponential Smoothing");
alpha=0.1;
beta=0.9;
psi=0.9;                                 /* a rate of decay in the trend */
xy(t,(data|miss(zeros(nahead,1),0))~damptf(data,alpha,beta,psi,nahead));




proc damptf(x,alpha,beta,psi,nahead);
   local n,L,T,m,mp,i;
   n=rows(x);
   L=zeros(n,1); T=zeros(n,1); m=zeros(n,1);
   L[1]=x[1];
   T[1]=0;
   i=2;
   do while i<=n;
      L[i]=alpha*x[i]+(1-alpha)*(L[i-1]+psi*T[i-1]);
      T[i]=beta*(L[i]-L[i-1])+(1-beta)*psi*T[i-1];
      m[i]=L[i-1]+T[i-1]; 
      i=i+1;
   endo;
   mp=miss(zeros(n-1,1),0)|m[n]|L[n]+cumsumc(psi^seqa(1,1,nahead))*T[n];
   m=m|miss(zeros(nahead,1),0);
   m[1]=miss(m[1],0);
   retp(m~mp);
endp;