*---------------------------------------------------------------*
|              (demo 2 A)                                       |
|  Using old f(D), verify that old and new level, slope,        |
| curvature match.                                              |
*---------------------------------------------------------------*;

data last; input Y @@; 
date=intnx('month','01dec83'd,_n_);
format date monyy.;
cards; 
10 . . 12 18 40 . 13 18 . . . 10 . 10 10
  ;
proc print; 
proc expand data=last from=month to=month out=out1; 
  convert Y = ynew;  id date;
data out1; merge out1 last; 
by date; proc plot data=out1; 
  plot Y*date="*" Ynew*date = "-" /overlay vpos=20 hpos=50; 
proc expand data=last from=month to=week out=out2 outest=spline;  
  convert Y = Ywk; id date;
proc print data=spline(obs=5); run;
data spline; set spline; if quad=. then quad=0; if cubic=. then cubic=0; 
L0=lag(constant); LL=lag(linear); LQ=lag(quad); LC=lag(cubic); 
D=date-lag(date); 
OldY=L0+LL*D+LQ*D*D+LC*D*D*D; 
Old1=LL+2*D*LQ + 3*D*D*LC;
Old2=2*LQ+6*D*LC; Quad2=quad*2; 
proc print; var D constant OldY Old1 Linear Old2 Quad2;
run;
/* ----------------------------------------output -----------------------------------------
                                       The SAS System    

     Obs     D     CONSTANT      OldY       Old1       LINEAR        Old2        Quad2

      1       .    -23.4075      .          .          1.07766      .           0.000000
      2      31     10.0000    10.0000     1.07766     1.07766     0.000000    -0.042864
      3     121     18.0000    18.0000     0.63630     0.63630     0.035569     0.035569
      4      31     40.0000    40.0000     0.30511     0.30511    -0.056936    -0.056936
      5      61     13.0000    13.0000    -0.20153    -0.20153     0.040325     0.040325
      6      31     18.0000    18.0000     0.26190     0.26190    -0.010426    -0.010426
      7     122     10.0000    10.0000    -0.08456    -0.08456     0.004746     0.004746
      8     120      6.5027     6.5027    -0.20305    -0.20305    -0.006721     0.000000
--------------------------------------------------------------------------------------*/