options crt nodate;
name bja 'ARMA(1,1) and MA(1) on Box-Jenkins series A';
? Box-Jenkins benchmark estimations -- p.239
? Box, G.E.P, and Jenkins, G. "Time Series Analysis:  Forecasting
?   and Control (revised edition)," (1976) Holden-Day.
? Notes:
? 1. Box-Jenkins use an "unconditional sum of squares" method which
?    is supposed to be roughly equivalent to exact ML.  It usually
?    does not match exactly, but it's fairly close.
?    For this reason, the TSP coefficients are not really a verified
?    benchmark.  A second independent package which estimates exact ML
?    ARIMA models is needed to reproduce these coefficients, to make
?    these benchmarks more certain.
? 2. The standard errors computed by TSP use the BFGS Hessian approximation,
?    with numeric derivatives.  They are not likely to be more accurate
?    than 1-2 digits relative to a Hessian computed from analytic second
?    derivatives.  The grad=c4 option is used to make the numeric
?    derivatives as accurate as possible.
load;

title 'ARMA(1,1)  with constant';
?       Box-Jenkins   TSP      Gauss3.2.35
?        p.239       BJEST        ARIMA
?  phi1    .92      .908685     .90865841
? (s.e.)  (.04)    (.023405)   (.04453284)
? theta1   .58      .575841     .57577387
? (s.e.)  (.08)    (.081197)   (.08675614)
? const.  1.45     1.55832     1.55876992 
? (s.e.)           (.399388)     
?  LogL            -50.7451    -50.745092
bjest(  const,nar=1,ndiff=0,nma=1,nocumpl,noplot,tol=1e-7,exactml,grad=c4) a;

title 'MA(1)  --  actually  ARIMA(0,1,1)';
?       Box-Jenkins   TSP      Gauss3.2.35
?        p.239       BJEST        ARIMA
? theta1   .70      .699384     .69936608
? (s.e.)  (.05)    (.064902)   (.05180149)
?  LogL            -53.5087    -53.508690
bjest(noconst,nar=0,ndiff=1,nma=1,nocumpl,noplot,tol=1e-7,exactml,grad=c4) a;
end;
noprint;
smpl 1,197;
read a;  ? p.525
17.0 16.6 16.3 16.1 17.1 16.9 16.8 17.4 17.1 17.0
16.7 17.4 17.2 17.4 17.4 17.0 17.3 17.2 17.4 16.8
17.1 17.4 17.4 17.5 17.4 17.6 17.4 17.3 17.0 17.8
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17.6 17.5 16.5 17.8 17.3 17.3 17.1 17.4 16.9 17.3
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18.0 18.2 17.6 17.8 17.7 17.2 17.4 ;