Consider the
AR(1)
series
x_(t)=\phi x_(t-1)+w_(t),
where
w_(t)
is white noise with variance
\sigma _(w)^(2)
and the model parameters are known. Suppose that we have observed
x_(1)
and
x_(3)
, and we would like to estimate the missing value
x_(2)
. Find the best linear predictor of
x_(2)
in terms of
x_(1),x_(3)
and
\phi
.