[Gretl-users] Re: ARMAX prediction/fitted values function ESTIMATES
On Mon, Jul 20, 2026 at 3:20 AM Sven Schreiber
<sven.schreiber(a)fu-berlin.de> wrote:
Am 19.07.2026 um 15:53 schrieb Brian Revell:
Humour me please. Let us suppose we have an ARMAX(1,0,0) model with 2 independent
variables and a constant.
ie (1-ΦB)Yt = α +µ1*X1t +µ2*X2t where B is the lag or backshift operator
Assuming Φ is positive this is equivalent to
Yt =α + Φ*Yt-1 +µ1*X1t +µ2*X2t
which is relatively straightforward to check against Gretl output using the estimated
coefficients and relevant rhs variables .However, the results of doing so do not
correspond to the predicted or fitted values from Gretl.
I think section 31.2 of the user guide could be relevant here, which talks explicitly
about ARMAX models and their subtleties.
Yes: see the explanation of the difference between equations 31.2 and
31.3. Here's an example.
<hansl>
open data9-7
# OLS
ols QNC 0 QNC(-1) PRICE INCOME
# eq 31.3, conditional ML
arma 1 0 ; QNC 0 PRICE INCOME --cond
# eq 31.2, ML
arma 1 0 ; QNC 0 PRICE INCOME
arma 1 0 ; QNC 0 PRICE INCOME --x-13
</hans>
Allin