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.stack.imgur.com/Q7B8c.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.
The bounty is to expire quite soon. So I'd be happy if some could at least give me one answer to my questions. It will help me a lot.
Why is nobody answering the questions? Are they not clear enough? If so, please tell me. I think they are important and fundamental as the concept of stationarity is quite important.