Are there any rules when it comes to determining the Order and the Seasonal Order in a SARIMA?

Question

Are there any rules when it comes to determining the Order and the Seasonal Order in a SARIMA?

I have noticed that when I use StatsModels in Python I can't choose a seasonal lag that is below or equal to the number of AR lags.

Example:

I am running a SARIMA with order (3,1,3) and seasonal order (3,1,3,3).

This generates an error: ValueError: Invalid model: autoregressive lag(s) {3} are in both the seasonal and non-seasonal autoregressive components.

Answer 1

• Specifying an order of (3, *, *) includes lags 1, 2, and 3
• Specifying a seasonal order of (3,,,3) includes lags 3, 6, 9, and 12.

By specifying this model, you would be including the third lag twice, which can cause numerical problems when estimating the parameters.

Instead, you should specify: order=(2, 1, 3) and seasonal_order=(3, 1, 3, 3). Then you will include the third lag as you want, but you won't have a duplicate.