Series from two sources (DK §3.10.3)
====================================

A survey estimate :math:`y_t` of unemployment, subject to survey error, and
an accurately measured related count :math:`x_t` (Harvey and Chung 2000),
modelled jointly with correlated local linear trends (DK eq. 3.49):

.. math::

   (y_t, x_t)' = \mu_t + \varepsilon_t, \quad
   \mu_{t+1} = \mu_t + \nu_t + \xi_t, \quad
   \nu_{t+1} = \nu_t + \zeta_t,

with full 2 × 2 covariances. The count is available a month before the
survey, which enters as a missing survey value (DK §4.10).

DK give no data; the example simulates them from the model, fits it, and
compares the estimates of the survey's level with those of a univariate
model.

Results
-------

Using the count lowers the root mean squared error of the smoothed level
from 0.353 to 0.307 and narrows the interval of the latest month's level,
where the survey is missing, from ±0.61 to ±0.57. With 120 observations
and estimated covariances the gain is modest; it grows with the
correlation between the two levels.

Program
-------

.. literalinclude:: ../../example/dk_3_10_3_two_sources.f90
   :language: fortran

Output
------

.. literalinclude:: output/dk_3_10_3_two_sources.txt
   :language: text