# Does Weak stationarity imply ergodicity ?

My intuition of ergodicity is the Law of Large Numbers for time series i.e. Given sufficient, data points, their mean and standard deviation would converge to population mean and standard deviation.

Does weak stationarity imply this inherently? Weak stationarity says the mean and standard deviation do not vary with time.

If it weak stationarity does imply, then why is the concept of ergodicity necessary at all ?

• – Alex C Jun 4 '18 at 4:42