/* Zero Lag Exponential Moving Average ZLEMA(k) */
new; cls;
let data[50,1]=
      60
      61
      60
      62
      60
      63
      64
      65
      69
      70
      69
      66
      64
      64
      62
      64
      65
      55
      53
      57
      60
      58
      63
      63
      63
      68
      69
      69
      68
      69
      70
      67
      66
      67
      68
      69
      69
      77
      80
      80
      78
      76
      76
      72
      71
      70
      73
      71
      78
      80
;
data=rev(data);               /* original data in reverse order */
t=seqa(1,1,rows(data));

library pgraph;
graphset;
_pltype=6;
_plegctl=1;
_plegstr="actual\000ZLEMA(5)\000ZLEMA(9)";
title("Zero Lag Exponential Moving Average");
xy(t,data~zlema(data,5)~zlema(data,9));        /* parameter k is odd */




proc zlema(x,k);
   local alpha,lag,i,m;
   alpha=2/(k+1);
   lag=floor((k-1)/2);
   m=zeros(rows(x),cols(x));
   m[1,.]=x[1,.];
   i=2;
   do while i<=lag;
      m[i,.]=alpha*x[i,.]+(1-alpha)*m[i-1,.];
      i=i+1;
   endo;
   i=lag+1;
   do while i<=rows(x);
      m[i.,]=alpha*(2*x[i,.]-x[i-lag,.])+(1-alpha)*m[i-1,.];
      i=i+1;
   endo;
   retp(m);
endp;