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st: arima predicted value

From   Rita Luk <>
To   "''" <>
Subject   st: arima predicted value
Date   Mon, 7 Jul 2003 01:51:47 -0400

Hi Statlist,

In ARIMA, how to compute the predicted value of a differenced time series
within estimate sample (not interested in forecasting out of sample) ?

Using monthly data of 120 observations(n=120), I estimate arima (0,1,1)
model:  Dy=a(t)-theta*a(t-1).
I suppose PREDICT yhat, XB is computed from theta*a(t-1).  Upon checking, it
is so except for the first nonzero predicted value(n=3) which has a
substantial difference of (yhat-theta*a(t-1)=-0.65) .

When estimate Seasonal arima (0,1,1)12: S12.y=a(t)-theta*a(t-12).
Again suppose PREDICT Yhat, XB is computed from theta*a(t-12). The first
nonzero predicted values appears in n=25. When comparing yhat with
theta*a(t-12), the differences are large (greater than 10) in n=25 to n=36.
The differences shrink when it moves down the time series, and are close to
zero among the last few observations.

Would you give me a clue on how exactly the predict value in arima are
computed ?

Thank you for your help.

Rita Luk
Ontario Tobacco Research Unit
Toronto, Canada
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