Checking for seasonality after residual serial correlation is no longer significant?

Can anyone answer why the text indicates to check for seasonality only after residual serial correlation (autocorrelation) is no longer significant in the AR model?
If autocorrelation is no longer significant in the AR model, doesn’t this imply that there is also no seasonality?
For example, I would think that upon finding significant autocorrelation in an AR(1) model, we decide whether or not to use AR(2) or seasonality lag depending on a) the number and b) the order of the autocorrelation in the errors in an AR(1) model…

Hi,
Could you indicate where you saw this problem?

At page 431 (volume 1) of the official curriculum you will find suggested steps in time series regression.

Regards.

Hi. I am referring specifically to page 432 of the 2020 text - step 7 where it starts off, “Your next move is to check for seasonality…”. This follows step 6, which calls for using an AR(2) model if significant serial correlation in the residuals are found in the AR(1) model.

Good morning,

My understanding (English is not my mother tongue) is that it is the description of an iterative process.

You begin with a simple model and add lags, add/remove explanatory variables until you have eliminated problems such as autocorrelation and multicollinearity.

I hope this help.

Regards