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According to this question Is every non stationary series convertible to a stationary series through differencing I already know that differencing isn't enough to make every non-stationary series stationary. However, we have more tools for making a time series stationary (detrending, removing seasonality, etc.), so is there any time series that we cannot make (by using all possible tools) stationary?

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    $\begingroup$ "Time series" has two distinct meanings: as a kind of stochastic process or as a single realization of such a process. Which meaning do you have in mind? What kind of stationarity do you mean--strict, first order, second order, or something else? What set of procedures would you consider to be "possible tools"? $\endgroup$
    – whuber
    Jul 2, 2020 at 15:46
  • $\begingroup$ I believe that stationarity refers to processes. However, in reality, we can observe only the realizations, and test stationarity based only on them, so I'm not sure what my answer should be. $\endgroup$
    – ononono
    Jul 2, 2020 at 16:05
  • $\begingroup$ Okay, so let's focus on processes. What definition of "stationary" do you intend us to apply and--most importantly--what specifically is your set of "possible tools"? $\endgroup$
    – whuber
    Jul 2, 2020 at 16:07
  • $\begingroup$ Weakly stationarity. The tools that I was thinking about are differencing, removing seasonality, etc. I'm not sure if it is possible to use them directly into the stochastic process. The general idea behind the question is if the methods proposed by econometricians or other TSA specialists allow us to model every time series. $\endgroup$
    – ononono
    Jul 2, 2020 at 16:51

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