Advanced Analytical Theory and Methods: Time Series Analysis - Data Science and Big Data Analytics - page 342

arima_1 <- arima (gas_prod,
order=c(0,1,0),
seasonal = list(order=c(1,0,0),period=12))
arima_1
Series: gas_prod
ARIMA(0,1,0)(1,0,0)[12]
Coefficients:
sar1
0.8335
s.e. 0.0324
sigma^2 estimated as 37.29: log likelihood=-778.69
AIC=1561.38 AICc=1561.43 BIC=1568.33
The value of the coefficient for the seasonal AR(1) model is estimated to be 0.8335
with a standard error of 0.0324. Because the estimate is several standard errors
away from zero, this coefficient is considered significant. The output from this first
pass ARIMA analysis is stored in the variable arima_1 , which contains several
useful quantities including the residuals. The next step is to examine the residuals
from fitting the (0,1,0) × (1,0,0) 12 ARIMA model. The ACF and PACF plots of the
residuals are provided in Figures 8.15 and 8.16 , respectively.
# examine ACF and PACF of the (0,1,0)x(1,0,0)12 residuals
acf(arima_1$residuals, xaxp = c(0, 48, 4), lag.max=48,
main="")
pacf(arima_1$residuals, xaxp = c(0, 48, 4), lag.max=48,
main="")