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st: ARMA forecasting

Subject   st: ARMA forecasting
Date   Sun, 25 Feb 2007 19:00:02 -0500

Hello all

I'm trying to fit some ARMA models to some time-series data I have
and trying to make one-step-ahead forecasts with the following

arima x, arima(1,0,0) //a simple AR(1) model
predict xhat, xb

Suppose the constant is estimated to be .4 and the autoregressive
parameter is estimated to be .25; now I want to calculate
one-step-ahead predictions and thats what I think I'm using the
<predict> command for. However, the <xhat> I get by using the
<predict> command doesnt tie in with my notion of what the
predicted values should be. For example, (from my limited knowledge
of time series), I think

E(x1 | x0) should just be = .4
E(x2 | x1, x0) should be = .4 + (.25*x1)
E(x3 | x2, x1, x0) should be = .4 + (.25*x2) and so on

(Note: these are just in-sample one-step-ahead forecasts. My actual
time series is 40 observations long and the parameter estimates
given above are for AR estimation done on the entire 40

However, the stata outputs for <xhat> using the predict command dont
match up with the above.

I'm quite puzzled about this. Any help would be much appreciated.


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