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.
This exercise is part of the course
ARIMA Models in R
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