Could you explain why AR models do better for stationary processes & do poorly for non stationary processes?
Sorry for the late reply!
Essentially, AR, ARMA, ARMAX and similar non-integrated models were created assuming we have stationarity. It’s because if we don’t have certain fixed restrictions throughout the data set, then modeling it becomes close to impossible. The idea is that stationarity ensures there is some pattern that can be modeled, so most (if not all) time series analysis and analytics just assumes stationarity as given.
Of course, equivalent integrated models were developed so that even when a data set is non-stationary, we can always attempt to model it. Hence, we need models like the ARIMA and ARIMAX.
Hope this helps!