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@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