/* Polynomial OLS Overfit (order=1 through 8 or 9) */
/* Data from Holton(2003)"Value-at-Risk" */
new; cls;
let data[10,2]=
1.1  2.14
1.4  2.60
2.5  1.15
2.7  1.19
3.2  1.88
3.6  1.55
4.1  2.65
4.3  3.80
4.5  4.46
4.9  6.35
;
x=data[.,1]; y=data[.,2];
call polynols(y,x,1);
call polynols(y,x,2);
call polynols(y,x,3);
call polynols(y,x,7);



proc polynols(y,x,order);
   local n,x1,i,beta,xx,xs,points,fmat;
/* creating X(=x1) */
   n=rows(x);
   x1=ones(n,1);
   i=1;
   do while i<=order;
     x1=x1~x^i;
     i=i+1;
   endo;
/* OLS    beta=inv(X'X)*X'y */
   beta=inv(x1'x1)*x1'y;
/* display the coefficients */
   print/lz "Polynomial order=" order;
   print "beta=" beta;
   print;
/* graph */
   points=200;                                                                 
   xx=seqa(minc(x),(maxc(x)-minc(x))/(points-1),points-1)|maxc(x);
   xs=ones(points,1);
   i=1;
   do while i<=order;
     xs=xs~xx^i;
     i=i+1;
   endo;
   library pgraph;
   graphset;
   pqgwin auto;
   begwind;
   window(1,1,0);
   scale(-0.05*(maxc(x)-minc(x))+minc(x)|maxc(x)+0.05*(maxc(x)-minc(x)),-0.25*(maxc(y)-minc(y))+minc(y)|maxc(y)+0.25*(maxc(y)-minc(y)));
   setwind(1);
      fmat="Polynomial (order= %*.*lG )";
      title(ftos(order,fmat,1,0));
      xy(xx,xs*beta);
   setwind(1);
      _plctrl=-1;
      _pcolor=15;
      _psymsiz=1;
      xy(x,y);
   endwind;
   retp(xx~xs*beta);
endp;