/* Holt-Winters' Multiplicative Method */
/* (Forecast Smoothing) */
new; cls;
let data[12,1]=
23
25
36
31
26
28
48
36
31
42
53
43
;
t=seqa(1,1,rows(data));

library pgraph;
graphset;
_pltype=6;
_plegctl=1;
_plegstr="actual\000predicted";
title("Holt-Winters' Multiplicative Method");
alpha=0.3;
beta=0.3;
gam=0.5;
p=4;                                     /* number of periods in S */
xy(t,data~hwmul(data,alpha,beta,gam,p));




proc hwmul(x,alpha,beta,gam,p);
   local n,L,T,S,m,i;
   n=rows(x);
   L=zeros(n,1); T=zeros(n,1); S=zeros(n,1); m=zeros(n,1);
   S[1:p]=x[1:p]/meanc(x[1:p]);
   L[p]=x[p]/S[p];
   T[p]=0;
   i=p+1;
   do while i<=n;
      L[i]=alpha*(x[i]/S[i-p])+(1-alpha)*(L[i-1]+T[i-1]);
      T[i]=beta*(L[i]-L[i-1])+(1-beta)*T[i-1];
      S[i]=gam*(x[i]/L[i])+(1-gam)*S[i-p];
      m[i]=(L[i-1]+T[i-1])*S[i-p]; 
      i=i+1;
   endo;
   L[1:p-1]=miss(zeros(p-1,1),0);
   T[1:p-1]=miss(zeros(p-1,1),0);
   m[1:p]=miss(zeros(p,1),0);
   retp(m);
endp;