Front and rear seat passengers (DK §8.3)
========================================

The log of monthly front and rear seat passengers killed or seriously
injured, modelled jointly: each series has a local level, a fixed
trigonometric seasonal and an irregular, and the level and irregular
disturbances are correlated across the series (DK §3.3). Rear seat
passengers were not covered by the seat belt law, so they serve as a
control group (Harvey 1996).

Five models: before 1983 with a full-rank and a rank-one level covariance,
then all data with the law in both series, in the front seat series only,
and the latter with a rank-one level covariance. The rank-one models use a
common level with an estimated loading and an intercept for the rear seat
series (DK §3.3.2).

Results
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All five models match DK to every printed digit, including the intervention
coefficients: for example front seat -0.35630 (rmse 0.03655) with the rear
seat series as control, and -0.41557 (0.02621) with proportional levels.
The difference in log likelihood between models 1 and 2 is 2.689, as in DK.

Three points about DK's printed values:

* DK's text includes km travelled and the petrol price as regressors, but
  the printed estimates are those of the model without them. With the
  regressors the estimates differ; without them all five models match.
* The printed exponents are one too small: the irregular variances are
  :math:`\times 10^{-3}`, the level variances :math:`\times 10^{-4}`.
* Two covariances are misprinted: model 1's level covariance is 2.933, not
  2.993, and model 3's irregular covariance 4.593, not 4.493. DK's own
  correlations, 0.893 and 0.660, imply the corrected values.

Program
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.. literalinclude:: ../../example/dk_8_3_passengers.f90
   :language: fortran

Output
------

.. literalinclude:: output/dk_8_3_passengers.txt
   :language: text