(a)
(b)
(c)
Figure 4: ACF and PACF charts after twice differences and the residual series of the ARIMA(1,1,1)(0,1,1)12 model. (a) Once common difference ACF and PACF charts. In the once common difference ACF chart, when lag = 1, the autocorrelation coefficient broke through the confidence interval. In the once common difference PACF chart, when lag = 1, the partial autocorrelation coefficient broke through the confidence interval apparently, while the coefficient hardly broke through the confidence limit when lag = 2. (b) Once seasonal difference ACF and PACF charts. In the once seasonal difference PACF chart, the partial autocorrelation coefficient broke through the limitation apparently when lag = 1. (c) The residual error correlation, ACF, and PACF of the ARIMA(1,1,1)(0,1,1)12 model. This model fell in the confidence limit, and there was no obvious correlation.