/*-------------------------------------------------------
**  VRATIO.G --  Computes variance ratio statistics
**                 using ratio of k to one period variance
**                 uses simple sums.
**                   Variances are computed by dividing by T, not T-k!
**
**         Inputs:  x -- series, must be in first differences
**                  k -- maximum number of VR(k) to compute
**                  inc -- increment
**
**         Output:  3 X (k-1) vector of (k,VR(k),std(VR(k)));
**
-----------------------------------------------------------------*/
proc vratio(x,k,inc);
@local nn,x,k,vr,ik,iik,inc,v1,kmax,kk,xk,ikk;@
local nn,vr,ik,iik,v1,kmax,kk,xk,ikk;
nn=rows(x);
v1=((x-meanc(x))'(x-meanc(x)))/nn;
vr=zeros(k,3);
vr[.,1]=seqa(inc,inc,k);
ik=inc;
kmax=inc*k;
ikk=1;
do while ik<=kmax;
 xk=zeros(rows(x),1);
 kk=0;
 do while kk<ik;
  xk=xk+lag(x,kk);
  kk=kk+1;
 endo;
 xk=trimr(xk,(ik-1),0);
 vr[ikk,2]=((xk-meanc(xk))'(xk-meanc(xk)))/(v1*ik*nn);
 ikk=ikk+1;
 ik=ik+inc;
endo;
vr[.,3]=vr[.,2]./sqrt(.75*(nn/(vr[.,1]+1)));
retp(vr);
endp;