/* Adaptive Response Rate Exponential Smoothing(ADRES) */
/* (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)+1);

library pgraph;
graphset;
_pltype=6;
_plegctl=1;
_plegstr="actual\000predicted";
title("ADRES");
beta=0.2;
xy(t,(data|miss(0,0))~adres(data,beta));




proc adres(x,beta);
   local n,m,alpha,S,A,e,i,m1;
   n=rows(x);
   m=zeros(n+1,1);
   alpha=zeros(n,1); S=zeros(n,1); A=zeros(n,1); e=zeros(n,1);
   S[1]=0; A[1]=0;
   alpha[1]=1;
   i=2;
   do while i<=n; 
      m[i]=alpha[i-1]*x[i-1]+(1-alpha[i-1])*m[i-1];
      e[i]=x[i]-m[i];
      S[i]=beta*e[i]+(1-beta)*S[i-1];
      A[i]=beta*abs(e[i])+(1-beta)*A[i-1];
      alpha[i]=abs(S[i]/A[i]);
      i=i+1;
   endo;
   m[n+1]=alpha[n]*x[n]+(1-alpha[n])*m[n];
   m[1]=miss(0,0); e[1]=miss(0,0); alpha[1]=miss(0,0);
   retp(m);
endp;