Advanced Analytical Theory and Methods: Time Series Analysis - Data Science and Big Data Analytics - page 341

Figure 8.13 ACF of the differenced gasoline time series
Figure 8.14 PACF of the differenced gasoline time series
The dashed lines provide upper and lower bounds at a 95% significance level.
Any value of the ACF or PACF outside of these bounds indicates that the value is
significantly different from zero.
Figure 8.13 shows several significant ACF values. The slowly decaying ACF values
at lags 12, 24, 36, and 48 are of particular interest. A similar behavior in the ACF
was seen in Figure 8.3 , but for lags 1, 2, 3,… Figure 8.13 indicates a seasonal
autoregressive pattern every 12 months. Examining the PACF plot in Figure 8.14 ,
the PACF value at lag 12 is quite large, but the PACF values are close to zero at lags
24, 36, and 48. Thus, a seasonal AR(1) model with period = 12 will be considered.
It is often useful to address the seasonal portion of the overall ARMA model before
addressing the nonseasonal portion of the model.
The arima() function in R is used to fit a (0,1,0) × (1,0,0) 12 model. The analysis
is applied to the original time series variable, gas_prod . The differencing, d = 1, is
specified by the order = c(0,1,0) term.