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I read an article about arima forecasting and i said that before we forecast arima model, its stationarity has to be checked.

If the model is stationary, it is clear that forecasting converges to whatever the mean the model has.

However for ARIMA(p,d,q) where d>0 or some non-stationary ARIMA(p,0,q), we have to consider a drift of the model and it implies that the model has no convergence in long term.

So, if we want to forecast non-stationary ARIMA model, then do we have to transform to the model to be stationary and proceed forecasting and then transform back to the original data with the calculated forecasting value?

(I know that long-term forecasting using ARIAM is not very useful, but this question is just for understanding the context)

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It is too much too text so I take screenshots and the link to Rob Hynman's blog entry:

If you formulate the ARIMA model likes this: enter image description here

Then you get these long term forecasts: enter image description here

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