Re: [Gretl-users] (no subject)
On Fri, 14 Mar 2014, Sven Schreiber wrote:
Am 14.03.2014 09:50, schrieb michel.pouchain(a)univ-paris13.fr:
> Dear gretl users,
> I have an example for a
> little dynamic model like
> :
> y(t) =a0+a1*y(t-1)+a2*x(t)
> When I use, via the scroll menu, "prévisions" I have
> the choice beetween static oy dynamic forecats.
> When I use "dyn", the forecast for T+1 is not equal to the
> forecats(static) for T+1. Why ?
Do you mean the point forecasts or the standard errors / intervals? If
you really mean the point forecasts, my guess would be that there is
some small difference in the specification (sample) that you haven't
noticed, otherwise it would indeed be strange.
Showing the output would be helpful.
> And I like to know which
> formulas used for the standards error?
> I have use with (R) program the formulas given by Pagan Nicholls
> (1984). Like microfit5
>
The 'fcast' help says: "For static linear models standard errors are
computed using the method outlined by Davidson and MacKinnon (2004);
they incorporate both uncertainty due to the error process and parameter
uncertainty (summarized in the covariance matrix of the parameter
estimates). For dynamic models, forecast standard errors are computed
only in the case of a dynamic forecast, and they do not incorporate
parameter uncertainty. For nonlinear models, forecast standard errors
are not presently available."
Here's an example:
<hansl>
open data9-7
smpl ; -2
ols QNC const QNC(-1) INCOME
smpl --full
# static forecast
fcast 1990:3 1990:4 --static --quiet
series fc1 = $fcast
series fe1 = $fcerr
# default forecast (dynamic out of sample)
fcast 1990:3 1990:4 --quiet
series fc2 = $fcast
series fe2 = $fcerr
smpl 1990:3 1990:4
print fc1 fe1 fc2 fe2 -o
</hansl>
<partial-output>
fc1 fe1 fc2 fe2
1990:3 2561.975 281.4759 2561.975 272.0654
1990:4 2461.011 280.6808 2572.629 310.1355
</partial-output>
As regards point values, the two forecasts for 1990:3 (the first
out-of-sample observation) are equal. But the forecasts for 1990:4 are not
equal, because the static one uses observed QNC on the right-hand side
while the dynamic one uses forecast QNC.
The forecast standard errors are not equal even for 1990:3. This is
because of the point noted by Sven: our standard errors for dynamic
forecasts do not incorporate parameter uncertainty. Therefore, for 1990:3
the fe2 value is slightly smaller than fe1. For 1990:4, however, the fe2
is larger than fe1 -- naturally, since the uncertainty due to the error
process is compounded; the latter uncertainty comes to dominate as the
forecast horizon increases.
Allin Cottrell