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st: arima predicted value
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)
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
Thank you for your help.
Ontario Tobacco Research Unit
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