I am trying to fit an ARMA model in Python for a non-stationary series. Conceptually, is it possible that I difference the data to first convert it to stationary data, fit the model on this differenced data and then have the model forecast for the original series? If not, what if I get forecast for the differenced data and do some manipulation to convert that forecasted differenced series to forecasted series at original level. How do I achieve this?


1 Answer 1


Note that $X_{t+h}=X_t+\Delta X_{t+h}$ where $\Delta X_{t+h}$ is the first difference of $X$ at time point $t+h$: $\Delta X_{t+h}:=X_{t+h}-X_t$. If you have the original series $X_t$ and a forecast for the difference $\widehat{\Delta X_{t+h}}$, then the forecast for the original series at time $t+h$ is $\hat X_{t+h}=X_t+\widehat{\Delta X_{t+h}}$. You simply add the forecasted values to the original series.

  • $\begingroup$ Thanks for your answer. Is this what happens at the backend of an ARIMA model where we supply certain degrees of differencing a.k.a integrations? $\endgroup$ Nov 30, 2020 at 23:54
  • $\begingroup$ @ShahzebNaveed, yes, I think so. $\endgroup$ Dec 1, 2020 at 7:53

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