AR(4) vs AR(1) with seasonal lagged 4th term


I am a bit confused…

Let’s say we have the following time series

ln(Xt)= b0 + b1 ln(Xt-1) + b4 ln(Xt-4) + et

Would you classify this as an AR(4) with coefficients b2=b3=0 or as an AR(1) with a seasonal lagged 4 term?

What is the thinking process behind the decision?

Thank you in advance for your inputs…


i think it is AR(n), where n is the number of lag. I usually look at the biggest value of time series to determine how many lag there are. For example, t-1 is 1 lag, t-2 is 2 lag, and so on. the model you have is the AR(4) model, and b1 and b2 in this case should be 0. Please correct me if i’m wrong.

I think also that is an AR(4).

Just to add to my initial post:

This is regarding AR model with a seasonal lag…

Thank you both for your inputs…