P/ACF of pure seasonal models

In the video, you saw that a pure seasonal ARMA time series is correlated at the seasonal lags only. Consequently, the ACF and PACF behave as the nonseasonal counterparts, but at the seasonal lags, 1S, 2S, …, where S is the seasonal period (S = 12 for monthly data). As in the nonseasonal case, you have the pure seasonal table:

Behavior of the ACF and PACF for Pure SARMA Models

	AR(P)S	MA(Q)S	ARMA(P,Q)S
ACF*	Tails off at seasonal lags	Cuts off after lag QS	Tails off at seasonal lags
PACF*	Cuts off after lag PS	Tails off at seasonal lags	Tails off at seasonal lags

*The values at nonseasonal lags are zero.

We have plotted the true ACF and PACF of a pure seasonal model. Identify the model with the following abbreviations SAR(P)_S, SMA(Q)_S, or SARMA(P,Q)_S for the pure seasonal AR, MA or ARMA with seasonal period S, respectively.