Table 3.

Correlation analysis of residual error of 3 candidate models.

Lag	ARIMA(1,1,1)(0,1,0)12			ARIMA(1,1,1)(0,1,1)12			ARIMA(1,1,1)(1,1,0)12
	Autocorrelation	Box–Ljung value	P	Autocorrelation	Box–Ljung value	P	Autocorrelation	Box–Ljung value	P
1	−0.00	0.00	0.97	−0.02	0.04	0.84	−0.02	0.06	0.81
2	−0.06	0.41	0.82	0.01	0.05	0.98	0.01	0.06	0.97
3	0.06	0.76	0.86	0.02	0.08	0.99	0.07	0.69	0.88
4	−0.07	1.28	0.87	−0.10	1.24	0.87	−0.12	2.18	0.70
5	0.02	1.31	0.93	0.02	1.26	0.94	0.03	2.27	0.81
6	0.06	1.69	0.95	−0.03	1.38	0.97	0.03	2.37	0.88
7	0.02	1.75	0.97	0.00	1.38	0.99	−0.04	2.53	0.93
8	0.09	2.65	0.96	0.06	1.79	0.99	0.06	2.89	0.94
9	0.11	3.92	0.92	0.05	2.11	0.99	0.08	3.61	0.94
10	0.06	4.31	0.93	0.04	2.29	0.99	−0.02	3.66	0.96
11	0.07	4.92	0.94	0.07	2.93	0.99	0.11	5.21	0.92
12	−0.37	21.46	0.04	0.06	3.38	0.99	−0.02	5.26	0.95
13	−0.04	21.67	0.06	−0.12	5.19	0.97	−0.11	6.78	0.91
14	0.20	26.86	0.02	0.11	6.83	0.94	0.16	9.80	0.78
15	−0.00	26.86	0.03	−0.04	7.02	0.96	−0.04	9.97	0.82
16	−0.01	26.88	0.04	−0.04	7.20	0.97	−0.02	10.03	0.87

Note. The correlation analysis of residual error of ARIMA(1,1,1)(0,1,1)₁₂ and ARIMA(1,1,1)(1,1,0)₁₂ models showed that neither of them had statistical significance (P > 0.05), so there was no obvious correlation and residual series was white noise.