I have a theory question which never became completely clear to me. Reading Hamilton (1995) I understod that the stationarity requirement for time series data stands as the normality requirement for non time series (cross sectional data) before running an OLS because of the Central Limit Theorem. I have the following questions:
- Does normality imply stationarity and viceversa (I don't think so, as I happen to notice) and if not why?
- When a regression is run on a time series it is however checked that residuals are normal. Why not checking that they are stationary as well?
- If the single time series of a regression are non stationary, but the residuals are, then we should run an ECM. What about the normality assumption?