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Every now and then I come across a discussion of forecasting methods that mentions the topic of stationary time series vaguely without specifying that it is a question mainly in the context of ARMA and ARIMA models. But as far as I know, exponential smoothing models, GAMs (e.g. Facebook Prophets), ML based approaches, etc... none of these seem to require that the time series be made stationary before we model it.

Are there any other univariate models besides ARMA models that require stationarity?

Additionally, it doesn't make sense to me that ML based approaches don't require stationarity: Intuitively it seems to me that stabilizing the mean and the variance of a time series would allow an ML algorithm such as neural networks or random forests to perform much better at a forecasting task.

In fact it seems that it would be very difficult for an ML algorithm to work without the mean and the variance of the series being stable, since ML univariate time series models are auto-regressive.

So why isn't stationarity a requirement for ML based forecasting methods?

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  • $\begingroup$ If you have clear causal drivers, or seasonality, then the mean (and potentially the variance) may be quite nonstationary, and many statistical or ML methods will still work great, so I won't quite follow your second-to-last paragraph. $\endgroup$ – Stephan Kolassa Aug 3 '18 at 8:36
  • $\begingroup$ @StephanKolassa I was thinking about the univariate case (no causal drivers). My reasoning w/r to ML methods is that they are auto-regressive and therefore would require the stability of the mean and variance for the same reasons that AR(p) models do. I will try to edit for clarity. $\endgroup$ – Skander H. Aug 3 '18 at 13:43

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