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I am trying to find cointegrated relationships between N variables. However it could be possible that only M of them are cointegrated where M < N. If I use standard Johansen's test on N variables it fails and says that there is no cointegration relationship. At the moment, I am using a brute force approach where I select combinations of M variables from N variables and testing them for cointegration. Is there a better way? Any references to research papers would be very helpful.

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The Johansen test is precisely devised to find cointegration among subsets of variables, i.e., to tell if the rank is any value between 0 (no cointegration) and n-1 (all cointegrated). So your result would indicate that in your data, there is no subset of cointegrated variables.

Now it may well be the case that in the presence of a high number of variables, the Johansen test does not give the right answer, so you might want to look on smaller subsets. But selection of that smaller subset should be based on theory, not data mining: if you test all possible subsets, you might end up finding some cointegration, which could be due rather to the multiple testing problem...

Regarding empirical papers, I can think of Pesaran (2007), who is running a whole series of pairwise cointegration tests, this might help...

Pesaran (2007) 2007, A PairWise Approach to Testing for Output and Growth Convergence, Journal of Econometrics, Vol. 138, pp. 312-355

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