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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!

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1) "Making a time series stationary" is only required if you want to do something that assumes the time series to be stationary. As you correctly state, not everything you may want to do (such as clustering time series) requires this.

2) Technically, stationarity is a very strong assumption, and what is usually referred to as "making a time series stationary" in fact normally only can make it appear stationary, or rather remove obvious indications of non-stationarity. That the resulting time series is very often referred to as (truly) "stationary" after this kind of transformation seems inappropriate to me, although my point here is that this is inappropriate wording, not that as a course of action it'd be inappropriate (because apparent/approximate stationarity is the best we can get anyway).

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    $\begingroup$ It is a lot clearer to me now. Thank you very much for the explanation! $\endgroup$ – Elise Le May 15 at 13:10

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