/* Percent Difference Smoothing(another version) */
/* (Forecast Smoothing) Criteria: MSE */
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("Percent Difference Smoothing");
nperiod=4;
xy(t,data~pdiff2MAD(data));




proc pdiff2MAD(x);
   local n,m,e,i,j,nperiod,nperiodstar,MAD,MAD_1;
   n=rows(x);
   MAD_1=1e+8;
      j=1;
      do while j<=floor((n-1)/2);
         nperiod=j;
         m=zeros(n,1);
         i=nperiod*2+1;
         do while i<=n;
            m[i]=x[i-nperiod]*(x[i-nperiod]/x[i-nperiod*2]); 
            i=i+1;
         endo;
         e=x[nperiod*2+1:n]-m[nperiod*2+1:n];
         MAD=sumc(abs(e))/rows(e);
         if MAD<MAD_1;
            nperiodstar=nperiod;
            MAD_1=MAD;
         endif;
         call sleep(0.0001);
         print/lz "iteration" j "out of" floor((n-1)/2);;
         print/rz "nperiod=" nperiod;;
         print "         MAD=" MAD;
         j=j+1;
      endo;
   print;
   print/lz "nperiod*=" nperiodstar;
/* main */
   m=zeros(n,1);
   i=nperiodstar*2+1;
   do while i<=n;
      m[i]=x[i-nperiodstar]*(x[i-nperiodstar]/x[i-nperiodstar*2]); 
      i=i+1;
   endo;
   m[1:nperiodstar*2]=miss(zeros(nperiodstar*2,1),0);
   e=x[nperiodstar*2+1:n]-m[nperiodstar*2+1:n];
   MAD=sumc(abs(e))/rows(e);
   print/lz "MAD=" MAD;
   retp(m);
endp;