I am not sure how cointegration work for a single set of markets and not another. I really don't think that's the matter and that I mean no disrespect. What is of difficulty is that cointegration works *some* of the time and not others. My experience is that are fantastic for range bound action although not trending markets. All things considered, all LM methods are based on the foundation that a mean is there. This can't hold true over longer intervals.
I read an excellent excuse of unit roots as if they were describing a blood flow of a river.
Just like the flows of a river, the directional bias of the individual flows of a basket of currencies change. At particular points in the river, the flows are centering around a loion. AT some points they're currently accelerating away from this stage. This is the foundation of the unit root test.
I have not researched ADF in depth to comprehend what its calling but based on my fundamental understanding I don't believe this accurately helps us discovers unit roots where the ebbs and flows from the river are many. I believe we have to visit the versions or Johanneson to become accurate unit roots.
Next Im a huge believer in HTF analysis. If we discover a basket is cointegrated on bigger (h1 ) timeframes, it opens up the potential for trading on the shorter timeframes when information from these timeframes drops out of synch.
None of this has been accounted for in anything I have read so far. Neither has been rebalancing, range bound checks, SR, etc..
Cointegration is a tool. It is not the holy grail. Managing the tool effectively should get us to where we want to be get which is to find an automated bot that eliminates the need to watch the markets constantly and still operate profitably.
FX-- I sent you an email. I am game.