Re: [Gretl-users] Standard error for confidence intervals
Hi Francisco,
I have sent an e-mail to the mailing list, but I haven’t got so much
success, I am going to rewrite the question to make it more
understandable (I am not a native English speaker)
Sorry for not answering, I personally couldn't answer your question,
because I thought it was related to the implementation details of
Prais-Winsten. Now I think maybe your question was more general, see below.
Basically, I have a dynamic prediction and I do not know why the
standard error grows up (see below), does anybody have the formula or
any paper where I can look into, thanks
Not sure if this answers your question, but: It is perfectly normal that
the forecast uncertainty grows as one predicts the values of periods
that are farther in the future. Intuitively, it is typically easier to
predict what happens tomorrow (think of the weather) than to predict
what happens next month.
Slightly more formally, for a stationary variable the dynamic forecast
uncertainty will converge (for h\rightarrow\infty, where h is the
forecast horizon) to a constant value which is basically the variance of
the unconditional mean estimate.
For an integrated variable, however, the forecast uncertainty will grow
without bound.
As regards the detailed formulae, I don't exactly which are used in
gretl. Several variants are possible, with or without small-sample
corrections, with or without parameter uncertainty, etc. etc.
Maybe this helps nonetheless,
cheers,
sven