/* Double Exponential Moving Average DEMA(k) assuming alpha=2/(k+1)  */
/* Notice: Conventionally, this is not EMA of EMA :ema(ema(x,k),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\000DEMA(5)\000DEMA(10)";
title("Double Exponential Moving Average");
xy(t,data~dema(data,5)~dema(data,10));



proc dema(x,k);
   local m1,m2,m;
   m1=ema(x,k);
   m2=ema(ema(x,k),k);
   m=m1*2-m2;
   retp(m);
endp;

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