Re: [Gretl-users] Standard Errors of OOS ARIMA Forecast?
On Thu, 25 Aug 2011, Skipper Seabold wrote:
I'm estimating an ARMA(2,2) model from generated data using
gretl's
exact likelihood. When I forecast 10 periods out from the end of the
sample, the first 2 forecast standard errors are as I would expect.
However, after this the standard error of the prediction is larger
than the standard error of my series. I was under the impression that
this cannot be.
"This cannot be" only for a one-step ahead forecast. For an h-step
ahead forecast the error variance is \sigma^2 for the series times
(1 + \psi_1^2 + \psi_2^2 + ... + \psi_{h-1}^2) where the \psi's
are the coefficients of the infinite MA representation.
In the limit, you take the limit of the above summation, which is
finite if the process is stationary, but is in general -- and pretty
obviously -- greater than 1.
Allin Cottrell