# What are the pros and cons of letting a variable follow an AR(1) process versus letting a variable follow an AR(1) process in logs

I would like to know the pros and cons of letting a variable follow an AR(1) process versus letting a variable follow an AR(1) process in logs.

Any help would be appreciated!

Thank you!

It’s the general issue of whether you want to consider your variable in absolute deviation or percentage deviation (logs).

Dear Professor Pfeifer,

Ah make sense. Thank you.

Sincerely,

Eric

If you have an exogenous variable following an AR(1) process it might happen that steady state considerations influence your choice.

1. If you define the AR(1) in levels your variable will have a zero steady state.
2. If you define the AR(1) in log-levels your variable will have a steady state of 1.

Suppose your variable shows up somewhere in the denominator. Then you have to use option (2) since under option (1) the steady state is not well defined.

But to be honest, I haven’t seen such an exogeneous process appearing in the denominator.

@Max1 That’s not entirely true. Both specifications can accomodate a non-zero steady state. The level process can also accommodate a zero steady state.

You mean by including a constant into the AR(1)?

Yes. Also note that first order, linear and log-linear processes are equivalent. It mostly makes a difference at higher order.