Hello!

You raised some issues, I would like to draw your attention that stationarity and normality are two different issues. Stationary indicates that the statistical properties of the stochastic part of the process do not change over time. Accordingly, the TS with trends, or with seasonality, are not stationary. Normal TS is assumed when the TS observations are drawn from a normal distribution. This can be tested by either the Q-Q plot or any other normality tests (Skewness and Kurtosis Measures). You always can use transformation to achieve either normality or stationarity, but be careful with that.

Best. :)

Dear sister Fatma Abdelkhalek ,

Thank you for your reply, however, I know well the difference between the two issues; my question was: the normality tests should be applied on stationary time series or we can apply them on non-stationary time series?

Regards

Hello Chellai Fatih

You can always assume normality in case you have VERY large sample based on the CLT. However, If this is not the case, you better check the normality assumptions in either cases and see to what extent the normality is violated. Check the nortsTest package in R, it provides various tests for normality in TS. I hope this helpful.

Never assume anything and apply Jarquae and Bera test to both stationary and nonstationary. The major point we cannot prove stationarity or nonstationarity.

Hello , when do we use the granger casualty test and the cointergration test