[Gretl-users] Re: Recursive forecasts for Arima models
On Sun, 24 Nov 2024, Sven Schreiber wrote:
[W]hat gretl calls "recursive" -- and I hope I'm
getting this
right -- entails updating/re-estimating the model coefficients for
every new value, starting from very early in the original base
sample.
Yes, except that I think it might be more common to do this out of
sample, or at least not necessarily starting from very early in the
original base sample.
So T2 is not fixed anymore (and this could become computationally
expensive for non-OLS estimators).
Yes. Let me just emphasize that a k-step ahead forecast gives
E(y_{t|t-k})
so at time t it cannot use any observed data more recent than t-k.
Example:
<hansl>
open AWM18.gdt
h = 3
smpl --full
ols ldiff(YED) const ldiff(YED(-1))
fcast h --recursive # prints out many forecast values, each h-step
</hansl>
I'm noticing that the printout here has no values for the final
two observations - to be honest, I don't know why that is so, all
the necessary ingredients should be there. Can anybody explain
this, please?
The trouble here is that while this is a dynamic model, that's not
clear to gretl. Your on-the-fly specification of the lagged
dependent variable as the log-difference of something "hides" from
gretl the fact that it's the first lag of the dependent variable. If
you did this instead
<hansl>
open AWM18.gdt
h = 3
y = ldiff(YED)
ols y const y(-1)
fcast h --recursive
</hansl>
you'd get a dynamic forecast that runs to the end of the dataset.
Allin