I'm trying to interpret the results of the Johansen Cointegration test. This answer helped improve my understanding, but Im trying to figure why, in the case provided for that question, if the null is rejected for r<=2, then there is "over 99% confidence to say that all instruments A, B, and C are stationary by themselves" and there is no need to build a cointegrated portfolio? So, actually this tells us the same thing, in terms of the cointegrating relationship, as failing to reject r<=0, that is there is no cointegrating relationship at some confidence level?

Also, for the following two cases: 1) does rejecting r<=1 and not rejecting r<=2, and 2) rejecting r<=0 and not rejecting r<=1, technically not tell us anything different? In that, I mean, both tell us we have at least two or one linear combination that is cointegrated, but whether its 2 or 1 makes no difference as long as its not 3 or 0?


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