/* Percent Difference Smoothing */
/* (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~pdiffMSE(data));




proc pdiffMSE(x);
   local n,m,e,i,j,nperiod,nperiodstar,star,MSE,MSE_1;
   n=rows(x);
   MSE_1=1e+8;
      j=1;
      do while j<=n-2;
         nperiod=j;
         m=zeros(n,1);
         i=nperiod+2;
         do while i<=n;
            m[i]=x[i-1]*(x[i-1]/x[i-1-nperiod]); 
            i=i+1;
         endo;
         e=x[nperiod+2:n]-m[nperiod+2:n];
         MSE=sumc(e^2)/rows(e);
         if MSE<MSE_1;
            nperiodstar=nperiod;
            MSE_1=MSE;
         endif;
         call sleep(0.0001);
         print/lz "iteration" j "out of" n-2;;
         print/rz "nperiod=" nperiod;;
         print "         MSE=" MSE;
         j=j+1;
      endo;
   print;
   print/lz "nperiod*=" nperiodstar;
/* main */
   m=zeros(n,1);
   i=nperiodstar+2;
   do while i<=n;
      m[i]=x[i-1]*(x[i-1]/x[i-1-nperiodstar]); 
      i=i+1;
   endo;
   m[1:nperiodstar+1]=miss(zeros(nperiodstar+1,1),0);
   e=x[nperiodstar+2:n]-m[nperiodstar+2:n];
   MSE=sumc(e^2)/rows(e);
   print/lz "MSE=" MSE;
   retp(m);
endp;