Your one-step-ahead forecasts by hand are incorrect.
If y_t = b_0 + e_t; e_t = rho*e_t-1 + v_t
Then the forecast for time t is
y_t = b_0 + rho*(y_t-1 - b_0)
For example:
sysuse auto,clear
gen t =_n
tsset t
arima mpg , ar(1)
predict xb,xb
gen foo =[ARMA]_b[L1.]*(l.mpg- _b[_cons])+ _b[_cons]
l t mpg xb foo in 1/10
Scott
> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-
> statalist@hsphsun2.harvard.edu] On Behalf Of da2147@columbia.edu
> Sent: Sunday, February 25, 2007 6:00 PM
> To: statalist@hsphsun2.harvard.edu
> Subject: st: ARMA forecasting
>
> 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
> commands:
>
> 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
> observations.)
>
> 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.
>
> Thanks
> divya
>
>
>
>
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