Clarification on SAS ARIMA Manual (p. 209)

[sasalex2024]

Dear SAS Community,

I am referring to the SAS ARIMA manual, page 209 ("Stationarity and Input Series"). I find the following statement confusing, and I apologize if I lack the knowledge to fully understand it:

"If the inputs are nonstationary, the response series will be nonstationary, even though the noise process might be stationary."

The reason I find this confusing is that if we have a raw data series for Yt​ and Yt is stationary to begin with, then simply by regressing Yt​ on some nonstationary Xt​, it should not make original Yt​ nonstationary because Yt​ is a known and given series (assumed to be stationary). Does SAS refer to the fitted values of Yt​? Or is there something else I am missing?

Thank you for your help.

[Ksharp]

""If the inputs are nonstationary, the response series"
I think Here "inputs" is Yt and "response series" is fitted/predicted values of Yt​.
And better post it at Forecasting Forum, since it is about SAS/ETS .
https://communities.sas.com/t5/SAS-Forecasting-and-Econometrics/bd-p/forecasting_econometrics

[sasalex2024]

Thank you!

[sbxkoenk]

See "Forecasting & Econometrics" - board :

https://communities.sas.com/t5/SAS-Forecasting-and-Econometrics/Clarification-on-PROC-ARIMA-manual-p...

Koen