*
* Example 8.7.1 from pp 291-292
*
open data lake.dat
cal 1875
data(format=free,org=columns) 1875:1 1972:1 lake
*
boxjenk(ar=2,demean,maxl) lake
*
* This generates the dummy variable for the observations we want skipped.
*
set miss = t==17.or.t==24.or.t==31.or.t==38.or.t==45.or.t==52.or.$
 t==59.or.t==66.or.t==73.or.t==80
*
diff(center) lake / clake
*
* This does four iterations on the EM algorithm. The %IF(x,y,z) function returns
* y if the expression x evaluates to a non-zero, and z if it evaluates to zero.
*
set eseries = %if(miss,0.0,clake)
do iters=1,4
   boxjenk(ar=2,maxl,noprint) eseries
   *
   disp iters eseries(17) eseries(24) eseries(31) %beta(1) %beta(2) -2*%logl
   compute v0=1+%beta(1)**2+%beta(2)**2,v2=%beta(2)/v0,v1=(%beta(1)-%beta(1)*%beta(2))/v0
   set eseries = %if(miss,v2*(clake{2}+clake{-2})+v1*(clake{1}+clake{-1}),clake)
end do iters
*
* The BOXJENK can also directly estimate the model skipping over some set of
* observations. This is done either if the dependent variable has actual missing
* data in it, or if the SMPL option (a contraction of SaMPLe) is used to tag the
* observations which are to be included in the estimated sample. The results are
* slightly different because the EM algorithm used above is the modified
* version, which won't have quite the same stationary point as the full EM.
*
boxjenk(ar=2,demean,maxl,smpl=.not.miss) lake