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I did some cointegration tests on a 50 stocks sample, whith which I created pairs. I used the Engle-Granger approach and the Johansen approach, both of them gave me a high percentage of cointegrated pairs(45% and 96%). I'm fairly sure about the way I did the Engle-Granger test (OLS->get residual and test for stationnarity with ADF test), but a bit less for the Johansen test, which I modeled after an example in Jansen's book about machine learning. In the same book Jansen found less than 5 % of pairs were cointegrated.

Does anyone know how rare is cointegration ?

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    $\begingroup$ Extremely rare, in fact I would argue it only exists for extremely highly related stocks (for example a local listing and an ADR, different share classes of the same stock, two ETFs tracking the same or highly related index etc). Of course a statistical test like Engle-Granger may return a positive result, but that is highly sample dependent. I would bet that many pairs which pass the cointegration test in one period do not pass it in the previous or subsequent non-overlapping period. $\endgroup$ May 26, 2022 at 10:18
  • $\begingroup$ Thank you for your answer. It's good to know how rare it is, my results didn't feel right. Do you know of a way to confirm cointegration ? I tried to do it by doing the two tests and only accepting results confirmed by both. But there are still too many pairs. How can I filter ? $\endgroup$
    – Alec Ric
    May 26, 2022 at 10:54

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