# ARIMAX v. ARX Time Series Modeling

I need to build a time series model with explanatory variables, and ARIMAX seems to be the one that comes up most frequently in practice, based on my survey of related work.

I know ARX solves a similar problem, but I'm having trouble wrapping my mind around the practical differences in what an ARX representation of my data would have compared with an ARIMAX approach.

I know ARX lacks the moving average component, but I'm curious whether anyone can point me toward some best practice for choosing one approach over the other.

Are there certain characteristics in my data I should look for to make an informed decision?

Yes, there are characteristics. You can use a correlogram to inform you as to the error structure in your data. That will tell you whether or not your data needs to account for AR and/or MA terms. Also check for unit roots to tell you whether you need to difference the time series.

This link has a good introduction to analyzing the correlogram that shows the pattern for AR(1) process. It is charecterized by a declining or oscillating but declining values. Depending on whether or not you have positive or negative autocorrelation.

The ACF for an MA(1) process is below. It is characterized by one significant value and then non-significant oscillating values thereafter.

To tell if you need to do differencing you should use a test like the augmented dickey-fuller test to check for the unit roots (i.e. your data is integrated).

• Yes, thanks! I'm wondering what it is one looks for to know know whether data has AR or MA terms, other than just model selection metrics like AIC. Commented Feb 25, 2016 at 11:37
• I tried to more fully answer your question. If I succeeded remember to accept it. :)
– Ryan
Commented Feb 25, 2016 at 16:23
• The link you posted is dead. You don't know if they just updated the location by any chance, do you? Commented Aug 5, 2021 at 11:10
• Looks like they moved it around try this one instead online.stat.psu.edu/stat510/lesson/1/1.2
– Ryan
Commented Aug 6, 2021 at 12:17