From my experience, when a time series $T$ is integrated/has a unit-root, one cannot model it with an ARMA model can usually need to turn to the first difference of $T$ (or some research I read uses $ln(T)$).
However, I just realized recently that in R's
auto.arima function (under the "forecast" package), it is possible to run an ARIMA regression with covariates (by specifying the parameter
xreg) even if the time series is integrated (e.g. an ARIMA(2,1,2) process).
My question is:
Does this model still yield valid statistical results about the covariates' coefficients?
If valid, how does
auto.arimadeal with the integrated process? I think it is probably not taking the first difference, but am not sure what is it.