The Johansen trace and maximum eigenvalue statistics both have the same
null. (Rank(Pi)=r) but different alternatives. The alternative for the
trace test is
Rank(Pi) > r
The alternative for the maximum eigenvalue test is rank(Pi) = r+1.
On 26/10/06, javier garcia enriquez <javigarcia83(a)yahoo.es> wrote:
At this moment we are doing a cointegration analysis and a doubt has come
up about the nule hypothesis that your programme uses in the Johansen test.We
don´t know if the maximum eigenvalue uses the same nule hypothesis as the
trace contrast( as for instance, Eviews does) , I mean, if both of
them contrast the hypothesis that there are, at most, "r" cointegration
vectors or, on the contrary, as we have read in some papers, this is only
done by the trace one, while the maximum eigenvalue contrasts that there are
exactly "r" cointegration vectors.
What we want to know exactly is if in your programme both of them use the
same nule hypothesis ( at most "r" cointegration vectors) or the trace one
uses that one, while the maximum eigenvalue uses the other one ( exactly "r"
Seeing the results we have got, we think that both of them use the same
one cause, if it isn´t like that, the contrast of the maximum eigenvalue
would say it exists 0 and 1 cointegration vectors at the same time.
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John C Frain
Trinity College Dublin