As stated in the question title, I can't understand the logic behind making a time series stationary. I do understand that stationarity is a necessity if we want to do forecasting because we need a (almost) constant mean and variance.
But what if a time series itself doesn't exhibit any trend? For example, a sensor that collects motion signals in a room. It is unlikely that the motions from people going in and out and around in this room follow a trend. To me it doesn't make sense to "force" stationarity in something that is unpredictable itself. In this case, do we need to make the time series stationary before applying analysis?
Maybe stationarity is only necessary when we do forecasting. Do we also need it when doing clustering or anomaly detection?
I'm new in time series analysis, so I'm sorry if my question sounds dummy. I tried to look up the answers to this online but so far people mostly discuss about the how and not the why.
Thank you very much!