# Non stationary residuals from stationary regression

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?
• You can always fit an ARIMA model to your residuals. Rob Hyndman explains this in his blog post "The ARIMAX model muddle", which has been referenced a few times on CV. May 23 '17 at 11:59
• "Verified" stationarity includes also homoskedasticity separately for the dependent variable and the regressors? May 23 '17 at 12:37