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Exercise

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.

Instructions

50 XP

Possible answers