The Johanesen determination of cointegration rank uses a sequence of nested
hypotheses. The concept of nested hypotheses is not well explained in
econometrics texts. It is well covered in Johansen's text 'Likelihood-based
inference in cointegrated vector autoregressive models, Oxford University
The trace test is
H0(r) : at most r cointegrating vectors against the alternative of
H1(r): more than r cointegrating vectors
The maximum eigen value test
H0(r) exactly r cointegrating vectors
H1(r) exactly r+1 cointegrating vectors
Thus the trace test is nested. If using the trace test H0(r) is
rejected one can proceed to test H0(r+1). This can be done because the
tests are nested.
If you use the maximum eigen-value test and you reject H0(r) then it is not
logical to test H0(r+1) as you have already accepted this by rejecting
In practice the two tests are used to complement one another.
One should also pay attention to the economics of the situation. Often
economic arguements provide a strong rational for the determination of the
number of cointegrating vectors. These relationships do determine the long
run relationship between the economic variables. Johansen without theory is
dangerous. If there are two or more than two cointegrating vectors you
will have to use economic theory to identify them. You may of course test
overidentifying restrictions within a Johansen framework.
These finer points are not, in general well under stood by economists. I
hope that this provides some clarification.
On 22/12/06, javier garcia enriquez <javigarcia83(a)yahoo.es> wrote:
Peter Summers wrote:
What you really need to do is consult an econometrics textbook, not the gretl
Sorry, but I think you're wrong. If you have read the Johansen's article
and other autor's articles, you can see the topic that I question isn´t
clear in the literature, especially with the lambda max test. Depending what
software do you use, the null hypothesis is different and, in statistics,
the interpretation depends completely of the null hypothesis. So, to
interpretate Gretl´s or other program's output we really need the null
hypothesis that they use, don't you agree?
Thanks to all, especially to Allin and Merry Christmas
PD: sorry for my bad English :p
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John C Frain
Trinity College Dublin