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it fits a polynomial regression, with an order p, i.e. linear regression where the the x variable is expanded so p=1: Y ~ x p=2: Y ~ x + x^2 p=3: Y ~ x + x^2 + x^3 etc. and return residuals. Thus if there is some linear or nonlinear trend in the data, it will be removed


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One way I have checked for cointegration is to run the OLS model on 2 series and then just do the ADF test on the OLS.residuals. If the residuals are stationary, then the series are considered cointegrated.


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