options crt nodate;
name bjc 'MA(2) exact ML on 2 subsets of Box-Jenkins series C';
?
?  Original benchmarks from Osborn, Annals of Social and Economic Measurement
?  1976 p.85.  2nd and 7th sets of 28 obs. from Box-Jenkins series C,
?  actually ARIMA(0,2,2).  Osborn's original sign convention was
?  (1 + theta1*L + theta2*L), and the signs have been reversed here to
?  agree with TSP's sign convention (1 - theta1*L - theta2*L) .
?    These are the two subsets where the exact ML and conditional ML
?  estimates differ the most.
?
?  set         Osborn     TSP     Gauss3.2.35
?               p.85     BJEST       ARIMA
?   2  THETA1  -.22   -.221182    -.22114633
?      (s.e.)  (.20)  (.205289)   (.19576123)
?      THETA2   .37    .372750     .37269824
?      (s.e.)  (.23)  (.223281)   (.19584441)
?      LogL            21.1068     21.106797
?   7  THETA1   .98   .987521      .99005358
?      (s.e.)  (.16)  (.098934)       (.)
?      THETA2  -.99  -1.000000    -.99999976
?      (s.e.)  (.25)  (.071644)       (.)
?      LogL            35.5839     35.583664
load;
bjest(exactml,ndiff=2,nma=2,tol=1.e-7,nocumplo,noplot,grad=c4) x2;
bjest(exactml,ndiff=2,nma=2,tol=1.e-7,nocumplo,noplot,grad=c4) x7;
end;
noprint;
smpl 1,28;
load x2;  ? 2nd set of 28 obs on B-J series C
21.8 21.4
20.9 20.3 19.7 19.4 19.3 19.2 19.1 19.0 18.9 18.9
19.2 19.3 19.3 19.4 19.5 19.6 19.6 19.6 19.6 19.6
19.7 19.9 20.0 20.1 20.2 20.3
;
load x7;  ? 7th set of 28 obs on B-J series C
24.9 24.8 24.7 24.6 24.5 24.5 24.5 24.5 24.5 24.5 24.5
24.4 24.4 24.2 24.2 24.1 24.1 24 24 24
23.9 23.8 23.8 23.7 23.7 23.6 23.7 23.6
; end;