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I have a simple liner regression model, and I tried validating if the model fit for purposes.

One of the tests is Augmented-Dickey Fuller test on the residuals but the result of the test shows that the error term is not stationary, if I continue using this model, what would be the implication?

In general, if my model failed stationary test on the residuals, so what?

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    $\begingroup$ Hi: It means that the regression residuals have a unit root which means that the regression of the response versus the independent variable didn't result in stationary residuals. This means that response and the independent variable are NOT cointegrated. Any regression between them suffers from non-stationarity which means residuals don't have either constant mean or constant variance or both. This means that the OLS assumptions are not met and the OLS is meaningless. $\endgroup$
    – mlofton
    Commented Dec 13, 2023 at 5:32
  • $\begingroup$ @mlofton, this sounds like an answer. Why not post it as such? (At some point there was a discussion on Meta concerning the cases where a question is answered in the comments but no answer is posted as such. It is usually a good idea to avoid such cases and post a proper answer instead.) $\endgroup$ Commented Dec 13, 2023 at 7:21
  • $\begingroup$ @mlofton thanks. I think thats the answer i am looking for. $\endgroup$ Commented Dec 13, 2023 at 9:53
  • $\begingroup$ Why did you fit this test to begin with? $\endgroup$
    – AdamO
    Commented Dec 13, 2023 at 16:37
  • $\begingroup$ Hi Richard: Okay. I'll put it as an answer. Sometimes I don't put it because I don't know what the OP wants as far as detail. In this case, it seems to be enough. Thanks. $\endgroup$
    – mlofton
    Commented Dec 14, 2023 at 8:36

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Hi Abdul Mateen Hashim:

It means that the regression residuals have a unit root which means that the regression of the response versus the independent variable didn't result in stationary residuals. This means that response and the independent variable are NOT cointegrated. Any regression between them suffers from non-stationarity which means residuals don't have either constant mean or constant variance or both. This means that the OLS assumptions are not met and the OLS model is meaningless.

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