4:09 p.m.
Can one assume that the interval in the forecast GUI Analysis option of an
estimated model is a true prediction interval?. If indeed it is, it would
also be useful to be able to graph the prediction interval surrounding the
fitted function values as well as the forecast ones.
Brian J Revell
Professor Emeritus
Harper Adams University , Shropshire
Current Chair of Defra Economic Advisory Panel
Tel 01952 815237
Tel: +44 1952 728153
Mbl +44 7976 538712
University: +44 1952 815235
alt: email: bjrevell(a)harper-adams.ac.uk
9:50 a.m.
Am 09.10.2021 um 18:09 schrieb Brian Revell:
Can one assume that the interval in the forecast GUI Analysis option
of
an estimated model is a true prediction interval?. If indeed it is, it
would also be useful to be able to graph the prediction interval
surrounding the fitted function values as well as the forecast ones.
Sorry, I think you need to define/explain a little more what you mean by
"true prediction interval".
thanks
sven
12:39 p.m.
The word "true" was used to draw attention to the distinction between a
prediction interval for a specific forecast/future value of y arising from
a value x0 and a CI for the regression line in relation to the values of x
in the sample.
The standard error differs between former and latter viz
[image: image.png] defines the standard error of a prediction of y given
a specific value of x0 and
[image: image.png] defines the standard error for the values of y from the
values of x underlying the parameter estimate generating y|x
On Sun, 10 Oct 2021 at 10:50, Sven Schreiber <svetosch(a)gmx.net> wrote:
Am 09.10.2021 um 18:09 schrieb Brian Revell:
> Can one assume that the interval in the forecast GUI Analysis option of
> an estimated model is a true prediction interval?. If indeed it is, it
> would also be useful to be able to graph the prediction interval
> surrounding the fitted function values as well as the forecast ones.
Sorry, I think you need to define/explain a little more what you mean by
"true prediction interval".
thanks
sven
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7:52 a.m.
Am 10.10.2021 um 14:39 schrieb Brian Revell:
The word "true" was used to draw attention to the
distinction between
a prediction interval for a specific forecast/future value of y
arising from a value x0 and a CI for the regression line in relation
to the values of x in the sample.
...
If I interpret you correctly, then "CI for the regression line" would
reflect estimation uncertainty, which is also called parameter
uncertainty. (As opposed to the additinal aspect of innovation
uncertainty in forecasting.)
See the last paragraph of the reference for the "fcast" command (and
perhaps also a corresponding part of the guide) for a description of
what the forecast interval (the standard errors) encompasses; it depends
on the properties of the model. But it is always true that it is _not_
an application of the interval for the regression line in the sense above.
On Sun, 10 Oct 2021 at 10:50, Sven Schreiber <svetosch(a)gmx.net
<mailto:svetosch@gmx.net>> wrote:
Am 09.10.2021 um 18:09 schrieb Brian Revell:
> Can one assume that the interval in the forecast GUI Analysis
option of
> an estimated model is a true prediction interval?. If indeed it
is, it
> would also be useful to be able to graph the prediction interval
> surrounding the fitted function values as well as the forecast ones.
Here I understand you as asking for a graphical representation of the
parameter uncertainty of the estimated regression line. Or perhaps also
to disentangle the various uncertainty components of a forecast. I'm not
sure we have that. Spontaneously I'd say that for the case with more
than one regressor that would involve the same methods and algorithms as
for capturing that aspect in the forecasting case, which is certainly
feasible but not trivial in general. E.g., for the probably most
important case of dynamic forecasts core gretl does not cover parameter
uncertainty. (Basically one would need a bootstrap I think.)
These remarks are all for standard regressions. Since you have worked
with the StrucTiSM package in the past, let me be clear that issues are
somewhat different there. Were you talking about forecasts with StrucTiSM?
cheers
sven
8:28 a.m.
Hi Sven
no I was not using StrucTiSM in this case, but models specified and
estimated with OLS and ARMAX. The post estimation Analysis GUI options
include Forecasts . Exogenous variable projected values are provided for
both OLS and ARMAX variant forecasts The displayed results are
prediction std. error 95% interval So my question relates to
whether the std. error is that of the regression line or the predicted
values, which differs from the regression std. error.
Hope that is clear.
Brian
On Mon, 11 Oct 2021 at 08:52, Sven Schreiber <svetosch(a)gmx.net> wrote:
Am 10.10.2021 um 14:39 schrieb Brian Revell:
The word "true" was used to draw attention to the distinction between a
prediction interval for a specific forecast/future value of y arising from
a value x0 and a CI for the regression line in relation to the values of x
in the sample.
...
If I interpret you correctly, then "CI for the regression line" would
reflect estimation uncertainty, which is also called parameter uncertainty.
(As opposed to the additinal aspect of innovation uncertainty in
forecasting.)
See the last paragraph of the reference for the "fcast" command (and
perhaps also a corresponding part of the guide) for a description of what
the forecast interval (the standard errors) encompasses; it depends on the
properties of the model. But it is always true that it is _not_ an
application of the interval for the regression line in the sense above.
On Sun, 10 Oct 2021 at 10:50, Sven Schreiber <svetosch(a)gmx.net> wrote:
> Am 09.10.2021 um 18:09 schrieb Brian Revell:
> > Can one assume that the interval in the forecast GUI Analysis option of
> > an estimated model is a true prediction interval?. If indeed it is, it
> > would also be useful to be able to graph the prediction interval
> > surrounding the fitted function values as well as the forecast ones.
Here I understand you as asking for a graphical representation of the
parameter uncertainty of the estimated regression line. Or perhaps also to
disentangle the various uncertainty components of a forecast. I'm not sure
we have that. Spontaneously I'd say that for the case with more than one
regressor that would involve the same methods and algorithms as for
capturing that aspect in the forecasting case, which is certainly feasible
but not trivial in general. E.g., for the probably most important case of
dynamic forecasts core gretl does not cover parameter uncertainty.
(Basically one would need a bootstrap I think.)
These remarks are all for standard regressions. Since you have worked with
the StrucTiSM package in the past, let me be clear that issues are somewhat
different there. Were you talking about forecasts with StrucTiSM?
cheers
sven
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