*Bounty: 50*

*Bounty: 50*

I just started trying to undestand the notion of stationary in time series. Basically I have 2 questions:

- Can stationary time series contain regulary cycles and thus seasonality patterns? For exmaple in this tutorial it is stated that stationary time series can not have seasonal components (predicitable cycles) https://otexts.com/fpp2/stationarity.html whereas in this figures (https://i.imgur.com/3lKCxEn.png) the green time series that clearly has cycles (and thus seasonality) is labeled as ‘stationary’

(and I have seen these kind of figures quite often if you just google ‘stationary time series) - Can a stationary time series have periods with no fluctuations and periods with high fluctuations? As far as I understood the variance and the (aut)covarianz should not change over time making such a time series not stationary. But here in this picture (https://www.researchgate.net/profile/Hazrat_Ali3/publication/326619835/figure/fig10/AS:654171351044097@1532978012116/Non-stationary-and-stationary-time-series-As-CDR-activities-of-users-are-aggregated-on.png) the time series below is labeld as stationary altough it has periods with changing fluctuations.

I hope you can help me as I am confused about the concept of stationarity. I’d appreciate every comment.

Update: Someone has already given his/her comment stating the impression that the time series in the links that are labeled as stationary are not stationary (but those statements were made with uncertainties as the plots are sketchy; see comments below). I’d like to hear further impressions about the 2 questions. I’d be happy if you could state your point of views.