Re: [Gretl-devel] OLS Forecasting
On 08.02.2009 16:56, Allin Cottrell wrote:
On Sat, 7 Feb 2009, Riccardo (Jack) Lucchetti wrote:
> On Sat, 7 Feb 2009, Sven Schreiber wrote:
>
>> On 07.02.2009 20:35, Allin Cottrell wrote:
>>> 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...
> The key is "mean-stationary" . Remember we're talking about the
> forecasts on the level, while the statistical model is in
> differences...
I think I'm with Jack on this: if the user doesn't believe the
forecast error should grow without limit (as it does under the
approach I outlined) then he/she shouldn't be estimating a model
in differences?
Well I'm kind of shooting in the dark here because I'm not familiar with
what model setups we're talking about *exactly*. But it kind of sounded
that it was all about whether the dependent variable was in differences
or not. That, however, would not be enough to warrant an I(1) assumption
for the levels. For example, it's perfectly legitimate to formulate a
single-equation error-correction model for I(0) variables, and in that
case the left-hand side variable would appear in differences, but the
levels would be I(0), and still the model would *not* be mis-specified.
But as I said, I'm not sure whether such specifications are really
covered by the new confidence intervals. Just want to raise a warning sign.
cheers,
sven