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 Press, 1995. 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 H0(r). 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&gt; wrote: -- John C Frain Trinity College Dublin Dublin 2 Ireland www.tcd.ie/Economics/staff/frainj/home.html mailto:frainj@tcd.ie mailto:frainj@gmail.com