/* Regularized Exponential Moving Average REMA(k,lambda) */
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\000REMA(5,lambda)\000REMA(10,lambda)";
title("Regularized Exponential Moving Average(lambda=0.5)");
lambda=0.5;
xy(t,data~rema(data,5,lambda)~rema(data,10,lambda));



proc rema(x,k,lambda);
   local n,alpha,m,i;
   alpha=2/(k+1);
   m=zeros(rows(x),cols(x));
   m[1,.]=x[1,.];
   m[2,.]=alpha*x[2,.]+(1-alpha)*m[1,.];
   i=3;
   do while i<=rows(x);
      m[i,.]=(m[i-1,.]*(1+2*lambda)+alpha*(x[i,.]-m[i-1,.])-lambda*m[i-2,.])/(1+lambda);
      i=i+1;
   endo;
   retp(m);
endp;