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If you believe the process $Y_t$ to be stationary, you can try to profit from it via a mean-reversion strategy or any other way that exploits the stationarity. It doesn't matter whether $Y_t$ is obtained as a cointegrational combination of a few non-stationary processes, or as a linear combination of some processes that are stationary themselves. In the ...

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1. There are a few differences between Cointegrated ADF test and Johansen test. First of all, the former is only suitable for a pair of two time series, while the latter is also applicable for cointegration test of any number of series. Secondly, ADF test will suggest different test results when we switch the sequence of the inputs, while Johansen test ...

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I can answer 2). It's either because you did something wrong with ADF test (it's impossible to say without knowing what exactly you did) or because you tested too many pairs w/o adjusting for multiplicity. The well-known paper of White is a good into into the issue.

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