Hi Tali,
PROC AUTOREG with the NLAG= option fits a regression model with an autoregressive error process. When available, lags of the structural residuals are multiplied with the AR coefficients in the fitted model to obtain the predicted values. When lagged structural residuals are no longer available, a best linear predicted of the structural residual is used. For details, please see the following sections of the PROC AUTOREG documentation:
https://go.documentation.sas.com/?docsetId=etsug&docsetTarget=etsug_autoreg_details02.htm&docsetVers...
https://go.documentation.sas.com/?docsetId=etsug&docsetTarget=etsug_autoreg_details51.htm&docsetVers...
The following SAS Note might also be of interest to you:
http://support.sas.com/kb/40135
If you want to fit a model with a lagged dependent regressor and other exogenous variables, then you might want to consider using PROC VARMAX to model and forecast your data. Please see the following section of the PROC VARMAX documentation for details:
https://go.documentation.sas.com/?docsetId=etsug&docsetVersion=15.1&docsetTarget=etsug_varmax_gettin...
I hope this helps!
DW