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.we...@gmail.com)
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