Thanks Sven,
you did answer my question: I tried to reproduce what you describe "by hand" and I come up with identical values as Gretl's ADF procedure. I was stupid not to figure it out by myself: of course we cannot compare AIC based on different sets of data.
Just for completeness I include the example you asked for.
All the best,
Matteo

PS: Here is the example

  k =  4: AIC = -324.082
  k =  3: AIC = -325.356
  k =  2: AIC = -327.350
  k =  1: AIC = -329.349
  k =  0: AIC = -322.373

Augmented Dickey-Fuller test for IBO

[...]

Augmented Dickey-Fuller regression
OLS, using observations 1974:3-1987:3 (T = 53)
Dependent variable: d_IBO

             coefficient   std. error   t-ratio   p-value
  -------------------------------------------------------
  const       0.00994959   0.00667146    1.491    0.1421
  IBO_1      −0.0686761    0.0415984    −1.651    0.4564
  d_IBO_1     0.389366     0.124332      3.132    0.0029  ***

  AIC: -345.238   BIC: -339.327   HQC: -342.965


Il 16/06/2017 18:24, Sven Schreiber ha scritto:
Am 16.06.2017 um 13:00 schrieb Matteo Pelagatti:
Dear Gretl users and developers,
I noticed that the AIC used in the lag selection procedure of the ADF test is different from the one reported under the regression results. Also, the lag selection would be different if based on the regression's AIC.

My questions are:
  "What formula is used for the selection procedure?",
"Why does it differ from the usual one?"

It might help if you could give a concrete example. Until then, my guess is that this is the same issue as in Ignacio's question just now: In the test-down procedure the (shortest) sample is kept fixed for all lags, while in the end result all available obs are used, thus leading to differences. This would not be gretl's fault.

cheers,
sven
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-- 
Matteo Pelagatti
Department of Economics, Management and Statistics
University of Milano-Bicocca
Via Bicocca degli Arcimboldi, 8
20126 Milano
Tel +39 02 6448.5834
http://www.statistica.unimib.it/utenti/p_matteo/