My concept here of recursive in an Arima model (2 0 1) for simplicity, with signifnt coeffcts on all parameters would be Xft+1=b1Xt+b2Xt-1+gErr t Xft+2=b1Xft+1 +b2Xt Xft+3 =b1Xft+2 +b2Xft+1 etc
ie the forecasts are endogenous. Of course with a difference operator in the Arima spec, the forecast equation becomes more complex when multiplied out. Brian On Sun, 24 Nov 2024, 11:27 Artur T., <ate...@posteo.de> wrote: > 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 > _______________________________________________ > Gretl-users mailing list -- gretl-users@gretlml.univpm.it > To unsubscribe send an email to gretl-users-le...@gretlml.univpm.it > Website: > https://gretlml.univpm.it/postorius/lists/gretl-users.gretlml.univpm.it/ >
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