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
