options crt nodate;
name bjfpac 'Box-Jenkins series F -- Partial AutoCorrelations';
? Box-Jenkins benchmarks
load;

title 'PAC - accurate and inaccurate versions';
?     Box-Jenkins    TSP/BJEST   TSP/BJIDENT
?     (uncond SSR)   (exact ML)  (Yule-Walker)  (std.error = .1195)
?  1     -.40        -.41908      -.38988
?  2      .19         .18734       .17971
?  3      .01         .010527      .0022645
?  4     -.07        -.072289     -.044277
?  5     -.07        -.069309     -.069406
?  6     -.15        -.15332      -.12062
?  7      .05         .046334      .019680
?  8      .00         .0042786     .0048884
?  9     -.10        -.11898      -.056497
? 10      .05         .065427      .0037055
? 11      .18         .16419       .14280
? 12     -.05        -.034254     -.0094066
? 13      .09         .077616      .091964
? 14      .18         .17602       .16693
? 15      .01         .016050     -.0012949
? (p.66 in Box-Jenkins(1976)).
mmake pacbj -.40 .19 .01 -.07 -.07 -.15 .05 .00 -.10 .05
             .18 -.05 .09 .18 .01;

? Yule-Walker method (subject to rounding error)
bjident(nlag=15,nlagp=15,nocumpl,noplot) f;

? OLS - more accurate method (pick off highest AR coefficient,
? same as conditional ML estimation -- does not impose stationarity)
copy @pac paco;
do p=1,15;
  set mp = -p;
  olsq(silent) f f(-1)-f(mp) c;
  set paco(p) = @coef(p);
enddo;

? most accurate method (pick off highest AR coefficient,
? using exact ML estimation)
copy @pac paca;
do p=1,15;
  bjest(nar=p,const,exactml,silent,
        nocumpl,noplot,tol=1e-7,grad=c4,maxit=50) f;
  set paca(p) = @coef(p);
enddo;
mmake pacs pacbj paca paco @pac;
print pacs;
end;
noprint;
smpl 1,70;
read f;  ? p.530 - yields from batch chemical process
47 64 23 71 38 64 55 41 59 48 71 35 57 40 58
44 80 55 37 74 51 57 50 60 45 57 50 45 25 59
50 71 56 74 50 58 45 54 36 54 48 55 45 57 50
62 44 64 43 52 38 59 55 41 53 49 34 35 54 45
68 38 50 60 39 59 40 57 54 23;