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If all that matters in forecasting is getting an accurate forecast then why is using non stationary data a problem. Say you use non stationary data to create a forecast that performs well in a pseudo out of sample forecasting test would it still be wrong to have it as your model?

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Problem is that in case the data are non-stationary your out of sample forecasts will usually be poor.

Even if it by random chance performs well in your training out of sample set, it is very likely that was just some good luck.

If you find that such model consistently outperforms models where you correct for non-stationarity you could use it. As you say in forecasting you only care about accuracy, it does not matter whether you get the accurate results from rigorous model or read them from dried up chicken bones.

This being said I would be extremely surprised if you would build forecasting model with non-stationary data that would consistently outperformed models where you correct for it.

PS: I assume above we are talking about models that cannot handle non-stationarity. Of course if we talk about some error correction model that can handle non-stationary series then there is no issue.

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  • $\begingroup$ I'm forecasting GDP. I have time series data going back 100 quarters on GDP and Copper prices. Both the GDP and the Price data fail a dicky fuller test. I took logs and first differences to apporximate a % change and tried forecasting with that. I first tried just an autoregressive model and then added lags of the price data too. Both performed far worse than just taking logs of GDP and Prices without correcting the stationarity issues. These are the only two forecasting models I've been taught I'm sure there are better options out there. $\endgroup$ Jul 22, 2022 at 6:47
  • $\begingroup$ @AlexStephenson as I said in the answer if you find those models consistently performing better use them. I don’t think it’s possible to get consistently lower forecasting errors with auto regressive model with unit root issue, but if you think you found such model you can use it $\endgroup$
    – 1muflon1
    Jul 22, 2022 at 7:40

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