I'm confused with the concept "stationarity".
I believe random walk is non-stationary and change (difference) in random walk is stationary. The characteristics of random walk are these below:
- long periods of apparent trends up or down
- sudden and unpredictable changes in direction.
On the other hand, this book mentions time series with aperiodic cyclic behavior are considered stationary. In my opinion, this "cyclic behavior" is very similar to the behavior of random walk.
Some cases can be confusing — a time series with cyclic behaviour (but with no trend or seasonality) is stationary. This is because the cycles are not of a fixed length, so before we observe the series we cannot be sure where the peaks and troughs of the cycles will be.
How should I interpret these passages?