ARIMA Model Changing With New Data I developed an ARIMA model with errors (https://robjhyndman.com/hyndsight/arimax/) to forecast the GDP growth of a small region. The issue is that the GDP values of past quarters and years change according to the corrections of the official statistical authority of the country, causing the model to change as well (e.g. the first model with the lowest AIC used to be an ARIMA(0,1,3), now with the new data it is an ARIMA(4,1,1)). My question now is how should I keep going? Should I stuck to the initial model or adapt the forecasts according to the new suggested model?
Thank you for any suggestion
 A: The updated data is presumably more correct, so it appears like a model fitted to the updated data is likely closer to the true data generating process, as well. So I would use the new model.
Then again, large changes in the forecast (note that different models may give forecasts that are not very different, at least at short horizons) would be a cause for concern. So I would at least take a look at the differences in the forecasts from the two models.
If two (or more) models are so equally reasonable that small changes in the data may make auto.arima() jump from one model to the other, it may also be worthwhile to use both models, by averaging the forecasts. As long as the order of integration is the same, you can also compare AICs and potentially use the AICs in a weighting scheme (e.g., Kolassa, 2011, IJF - sorry for the self-promotion). Note, however, that investing a lot of time in finding "optimal" weights may not help a lot (Claeskens et al., 2016, IJF).
Finally, if you have the time, you could also disable some of the computational shortcuts that auto.arima() takes, which may give you yet other models to play with, by setting stepwise=FALSE and/or approximation=FALSE.
