dear R and stats wizards:  I would like to estimate an AR1 model with
constant and measurement noise:

  true[t] = a + b*true[t-1] + noise1[t]
  observed[t] = true[t] + noise2[t]

(true is never observed.)  I am very interested in forecasting
observed[t+1]., and modestly interested in inferring b and true[t].  I have
a lot of data.  in truth, I really have a panel with thousands of
individuals, so I don't get the usual strong AR1 bias when b is close to 1.

my intuition is that a good forecast of observed[t+1] (and thus of true[t])
is a historical weighted average of past observed[t] values, with more
weights on more recent observeds, and in effect shrunk towards the long-run
mean.  by simulating the model, I can observe how the auto-corrollelogram
looks like, and fit it. however, both of these are amateurish---this
problem seems so canonical that it has probably been solved a gazillion
times.

could someone please point me to some simple textbook = howto treatments of
this problem and/or R packages that implement this?  feel free to point out
your own work...this way I can cite it.

regards,

/iaw
----
Ivo Welch (ivo.welch@gmail.com)

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