Re: [Gretl-devel] OLS Forecasting
On 07.02.2009 20:35, Allin Cottrell wrote:
On Sat, 7 Feb 2009, Allin Cottrell wrote:
> [Auto-integration of forecasts] is now implemented on a trial
> basis in CVS/snapshot, but only for single-equation OLS at this
> point.
Follow-up: At present, we produce forecast standard errors in this
case only if the model contains no dynamics (other than the
dynamics implied by the fact that the dependent variable is a
first difference). And in producing the standard errors we (a)
ignore parameter uncertainty and (b) assume a white-noise error
process. On that basis, we calculate
se(k) = sqrt(k*s2)
where k = 1,2,...n is the forecast step and s2 is the square of
the Standard Error of the Regression.
If this is rubbish -- or if there is a clearly better way to
proceed -- I hope Jack or Sven will tell me so!
Indeed it seems to me that this is not entirely correct in general; with
this formula the forecast uncertainty grows linearly (and thus w/o
bounds) irrespective of the property of the considered variable. But for
a mean-stationary variable the long-run forecast is just its mean, and
the associated confidence interval is finite. So in effect here it looks
as if you're assuming something like a random walk, and I'm not sure why
this assumption would be warranted in general. Just because the variable
was differenced by the user doesn't qualify IMHO.
cheers,
sven