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I was wondering, if I perform linear OLS regression with stationary (verified) time series $y_t$ on $x_{1t}$,$x_{2t}$:

  • can the residuals be non-stationary?
  • it is not part of a list of Gauss-Markov assumption that the residuals of the OLS linear regression must be stationary so we usually don't need to perform stationarity test on residuals as a part of time series linear OLS regression?
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If your independent variables are non-stationary and the dependent variable is then the residuals will end up being non-stationary.

Gauss-Markov conditions require stationary of residuals for time series.

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  • $\begingroup$ But what if all my time series are stationary? And in the list of assumptions i don't see explicitly stationary of residuals as requirement. I believe i don't understand something. $\endgroup$ May 23 '17 at 11:34
  • $\begingroup$ @AlexanderShubert, the requirements of Gauss MArkov do not spell it out literally, but the residuals are stationary. For instance, TS-4 in my link tells you that the variance is constant, which is one of the conditions of stationary series $\endgroup$
    – Aksakal
    May 23 '17 at 13:24

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