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I have a time series based on 'power', as given by a sensor. The power changes as the thing it is measuring changes, typically with the distance of the thing being measured from the sensor.

If I understand correctly, a time series is not stationary if the mean changes over time. Since this thing we are measuring spends time at various distances from the sensor, the mean of the power changes (the thing being measured moves around pretty much randomly).

I'm interested in how the power changes, which directly affects how the mean changes. Is it true I cannot treat this series like a stationary series?

Richard Hardy
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HorseHair
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    The thing you are interested in (changes in power) is rooted in the lack of stationarity, so unless you want to pretend that it's stationary as some sort of null hypothesis, then no. You might be able to treat the differenced timeseries (where $t'_i = t_i - t_{i-1}$) as stationary, although I'm not sure if that's what you want... what exactly are you trying to do here? – jon_simon Sep 12 '17 at 22:45
  • @jon_simon - Why wouldn't I want to use the differenced timeseries (what restrictions may apply?) This is one input for a machine learning algorithm that tries to distinguish between different (power sources) being sensed. – HorseHair Sep 13 '17 at 00:17
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    If the power value itself had been relevant to the problem you were trying to solve, then differencing would have removed the most important piece of information. But given your (now-articulated) use-case, using the differenced timeseries does indeed sound like a good idea. – jon_simon Sep 13 '17 at 01:02
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    First differencing may or may not be fine from a machine learning perspective, but differencing a series that is not integrated is certainty problematic from the statistical perspective. Differencing should only be applied on integrated time series as otherwise you get into the problem of overdiffercing and its consequences. – Richard Hardy Sep 13 '17 at 05:18
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    Regarding stationarity, it depends on how the object moves. If it is drawn by some physical law to some equilibrium location, then the measurements can be stationary. If it moves like a random walk, then the measurements will likely be a random walk themselves, and thus nonstationary. Moreover, in the latter occasion first-differencing the series could make it stationary. – Richard Hardy Sep 13 '17 at 05:21
  • @RichardHardy - Thank you for the information. https://stats.stackexchange.com/questions/303019/what-is-an-integrated-time-series – HorseHair Sep 13 '17 at 18:48

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