# Time Series Stationarity

I know there are many questions here about stationary tests etc however I have a question about general time series modeling.

Is stationarity important for all models? For example, if I model a time series using a Gaussian process of the form

$$y_t = f(y_{t-1}) + \epsilon$$

where

$$f \sim GP(.,.)$$

Should I use differencing? If I should, how do I transform my predictions on the differenced time series back to the original axis?