# Polynomial distributed lag AR model specification

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.

• What does PDL stand for? Dec 31, 2016 at 8:49
• There are models where lags of both dependent and independent variables are included, e.g. autoregressive distributed lag (ARDL) model. Also, what does PDL stand for? Dec 31, 2016 at 9:01
• Thank you for sharing the info, that explains a lot. PDL is short for polynomial distributed lag, could be finite or infinite. Dec 31, 2016 at 15:14

## 1 Answer

[A]re there ever occasions where one specifies a lagged term of a independent variable alongside an AR term? <...> [C]ould someone please share what they feel the most appropriate name of that kind of model would be?

One model where lags of both dependent and independent variables are included is autoregressive distributed lag (ARDL) model. See e.g. Dave Giles' blog post "ARDL Models - Part I" for some details.

• Very informative, I glued to my eviews screen. Sorry for the late reply. So is it typical for the ARDL model lags to be of the same magnitude? With pdl, one can specify the polynomial order as well as finite or not. I wonder if any of these can be configured with ARDL. I haven't seen this covered yet. Jan 19, 2017 at 23:10
• @ArashHowaida, I do not remember seeing ARDL with infinite lag, and I do not know if this is available in existing software. Regarding the same magnitude, it must depend on the application. You can imagine situations where they could be similar and others where dissimilar. Sorry for not being able to give more definite answers. Jan 20, 2017 at 6:41