AR(1)+1 more seasonal lag Vs AR(2) models

[passme]

AR(1) model: Y=b0+b1 (Xt-1)
add a seasonal lag Xt-4 to the above AR(1) model results in a AR(1) model with additional lagged seasonal term.
my question is, how do we distinguish AR(1)+2 lagged term with AR(2) model.

 

[passme]

well I thought about it and i think this is how we distinguish bt them:
AR(1)+lagged term: the lagged term is not the immediate period prior to the existing lag.
AR(2): both lagged terms are neighbouring periods
AR(30): we will be looking at a regression with lagged term with Xt-1 all the way thru Xt-30
something like that.

 

[integraldx]

Ok lets say an AR(1) model is defined as: x(t) = a + b*x(t-1)
By adding an extra lag, what we mean in is x(t) = a + b*x(t-1) + c*x(t-4)
An AR(2) model is x(t) = a + b*x(t-2)
Thats what I’ve understood. Correct me if I’m wrong.

 

[Dreary]

passme, you got that right. The idea is that because of the seasonal effect, you want your model to predict the correct value due to the season. That means that an AR(4) model for quarterly data is same with or without seasonal effect! Yes?
How do you know there is seasonal effect? Look for a lag which has a relatively large autocorrelation value (or a significant t-stat).

 

[passme]

thax dreary for the confirmation. appretiate it