# Isn't this a AR(3)? Please discuss.

An analyst wants to model quarterly sales data using an autoregressive model. She has found that an AR(1) model with a seasonal lag has significant slope coefficients. She also finds that when the second and third lags are added to the model, all slope coefficients are significant too. Based on this, the best model to use would most likely be an: A) AR(0). B) AR(4). C) AR(1). D) AR(2).

I think it should be an AR(4), a second and third lag was added and the slope coefficients were still significant. I believe you have to keep adding lags until they are all insignificant

lol. I don’t think you have enough information yet except that they leave out AR(3). Based on above I would choose AR(3) also.

I went with AR(4) -which is correct- yet it seems it should be an AR(3)…

On the test I would go with AR(4) too probably for the same reasons you did.

I think a legitimate argument could be made for AR(2) or AR(4). The reasoning for AR(4) would be what Blkmoon noted. The reasoning for AR(2) is that AR(3) is the right answer, but AR(2) is the best answer. It is still significant when AR(4) has insignificant variables. Simpler is generally better and AR(2) probably explains the series just as well as AR(4) does. The idea behind using an AR(4) also could be that it is quarterly data. So if you go back four quarters you wouldn’t need to use a seasonal lag. So if I could use the AR(4) without the seasonal lag or AR(2) with one, I would probably use the AR(2). Questions like these are generally hard to answer in a multiple choice format b/c there are many different reasons that different models could be chosen.