[Gretl-users] Johansen

[Sven Schreiber]

Javier García schrieb:
> Then how is it that the nule hypothesis r = 0 and r = 1 are both
> accepted to the two contrasts? the only consistent hypothesis with the
> results is that both nule hypothesis is that the rank (pi) minor or
> equal to "r", because the rank can't be 0 and 1 at the same time.
>  

Ok this has nothing to do with gretl anymore, but anyway:

You can interpret each test individually as having <= in the null
hypothesis, no problem. However, to determine the rank (which normally
is what you want), you have to do a sequence of tests. Then, after
rejecting r=0 in a first test, the second test should better be
interpreted to have null hypothesis r=1. It does not make much sense to
postulate H_0: r<=1 for the second test, because you already rejected
r=0, so all that's left is r=1. (Of course, for the calculation of the
test statistics, it doesn't make any difference anyway.)

But, if you have already accepted the hypothesis of r=0 (against r>0),
then why on earth are you testing a rank of 1 against r>1? That is not a
consistent rank determination procedure.

HTH, Sven