[S] Possible Enhancements - prediction intervals

Bruce McCullough (BMCCULLO@fcc.gov)
Tue, 21 Apr 1998 10:02:38 -0500

Snipping from a couple posts:

[predict.glm, predict.lm have se.fit option
predict.lme, predict mlm do NOT have an se.fit option]
>> If you are making predictions, it seem sensible that se should be
>>available for the predictions.
>WORSE: non of the above PREDICT functions give se of the
>predictions, only the se of the expected values!

In all fairness to S-PLUS, we all know that under the regular
assumptions the standard error of the expected value of
the forecast is normal, so confidence intervals can be
derived easily. As to the predicted value itself, that is
another matter, because the predicted value is a sum of
products of stochastic quantities and, as such, does not
have an easily derived distribution. See Feldstein (1971)
on this point. There is a bootstrap method for obtaining
consistent confidence intervals in this situation (McCullough, 1996),
but it is nothing which can be easily implemented as
a generic method.

Feldstein, M. (1971), "The Error of Forecast in Econometric
Models when the Forecast-period Exogenous Variable
is Stochastic" Econometrica 39, 55-60

McCullough, B.D. (1996), "Consistent Forecast Intervals when
the Forecast-period Exogenous Variable is Stochastic"
J Forecasting 15, 293-304

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