Generally speaking, polynomial distributed lag (PDL) models deal with independent variables and autoregressive (AR) models deal with dependent variables (their errors), but are there ever occasions where one specifies a lagged term of a independent variable alongside an AR term? I have not come across this too much in the literature and I wasn't sure if it was because it's not a good idea, or if it was because it's too obvious and didn't need addressing. If it is common practice, could someone please share what they feel the most appropriate name of that kind of model would be? Would it be as straightforward as PDLAR?
I would like to hear what a few experts have to say about this.