[Gretl-users] Re: Recursive forecasts for Arima models
Am 24.11.24 um 11:59 schrieb Sven Schreiber:
Am 23.11.2024 um 18:02 schrieb Brian Revell:
> Is there any reason why recursive forecasts cannot be included in the
> ARIMA option for univariate modelling together with their confidence
> intervals when the model is truly univariate with no exogenous
> varisbles included in the specification Clearly post sample data the
> MA terms would drop out of the forecasts that would effectively only
> require the AR parameters and any differencing.
>
I'm wondering whether what you're trying to achieve is the same thing as
what's called "recursive" in gretl. Maybe it is, but the terminology can
be complex and not always universal.
Indeed, good point, Sven.
So: If you have a base sample from t=T1 to t=T2, and you estimate
your
Arima model on that sample, and then you want to create forecasts for
the out-of-sample range T2+1 through T2+h, for a certain positive
integer h, you can do that, but we wouldn't call it recursive. Example:
<hansl>
open AWM18.gdt
h = 3
smpl +0 -h # leave some obs for the forecasting range, T2 is now 2017:1
arima 1 1 1; log(YED)
fcast --dynamic --out-of-sample # prints out h=3 forecast values up to
2017:4
</hansl>
This is a forward-iterated forecast. Again, maybe this is _not_ what
you're actually trying to do, I just want to make sure there are no
misunderstandings, because sometimes people call this thing recursive.
We just discussed this internally, last week. The option --out-of-sample
is expected to produce for all out-of-sample observations after T2
forecasts, irrespective of the provided horizon. Actually, it currently
remains unclear, whether it should be allowed to provide an integer for
steps-ahead (the max. horizon) jointly with the --out-of-sample option.
In contrast, what 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. So T2
is not fixed anymore (and this could become computationally expensive
for non-OLS estimators). 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 think this part is buggy from the gretl side. Here is another example
for which also the last two observations are missing.
<hansl>
open AWM18.gdt
h = 3
smpl ; 2016:4
ols ldiff(YED) const ldiff(YED(-1)) --quiet
# ERROR: No oos forecasts shown
# No difference if omitting "--out-of-sample"
fcast h --recursive --out-of-sample
smpl 2017:1 $tmax
series fc = $fcast
# Only for the first 2 observations, forecasts are shown
# However, one would expect only a single h=3 forecast value at
# date 2017:3
print fc -o
</hansl>
Artur