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st: predict res, after ARIMA


From   "Richard Boylan" <rtboylan@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: predict res, after ARIMA
Date   Mon, 3 Nov 2008 11:19:28 -0600

The STATA manual states that predict res is the predicted innovation epsilon(t).

It is also my understanding that it is computed as the residual of the
prediction of the model:
res(t) =  y(t) - E_(t-1) y(t).

With finite sample, this is not the same as the forecast at time t of
res(t); i.e.,
E_t res(t) need to equal to y(t) - E_(t-1) y(t).  [By E_t, I mean the
expectation conditional on the values y(t), y(t-1), ..., y(0).]

For instance, is y(t) is MA(1) with no constant, E_t res(t) = E_t
y(t+1)/theta which in finite samples is different than y(t) - E_(t-1)
y_t.

Has anyone programmed E_t res(t)?
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