/* Single Exponential Smoothing where parameter alpha is automatically chosen. */
/* (Forecast Smoothing) Criteria: MAD */
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("Single Exponential Smoothing");
prec=0.01;
xy(t,data~sesMAD(data,prec));




proc sesMAD(x,prec);
   local n,m,e,i,j,alpha,alphastar,count,MAD,MAD_1;
   n=rows(x);
   MAD_1=1e+8;
   count=1;
      j=1;
      do while j<=(1/prec);
         alpha=prec*(j-1);
         m=zeros(n,1);
         m[1]=x[1];
         i=2;
         do while i<=n;
            m[i]=alpha*x[i-1]+(1-alpha)*m[i-1]; 
            i=i+1;
         endo;
         e=x[2:n]-m[2:n];
         MAD=sumc(abs(e))/rows(e);
         if MAD<MAD_1;
            alphastar=alpha;
            MAD_1=MAD;
         endif;
         call sleep(0.0001);
         print/lz "iteration" count "out of" (1/prec);;
         print/rz "alpha=" alpha;;
         print "         MAD=" MAD;
         count=count+1;
         j=j+1;
      endo;
   print;
   print/lz "alpha*=" alphastar;
/* main */
   m=zeros(n,1);
   m[1]=x[1];
   i=2;
   do while i<=n;
      m[i]=alphastar*x[i-1]+(1-alphastar)*m[i-1]; 
      i=i+1;
   endo;
   e=x[2:n]-m[2:n];
   MAD=sumc(abs(e))/rows(e);
   print/lz "MAD=" MAD;
   retp(m);
endp;