Table 3: Correlation analysis of residual error of 3 candidate models.

LagARIMA(1,1,1)(0,1,0)12ARIMA(1,1,1)(0,1,1)12ARIMA(1,1,1)(1,1,0)12
AutocorrelationBox–Ljung valueAutocorrelationBox–Ljung valueAutocorrelationBox–Ljung value

1−0.000.000.97−0.020.040.84−0.020.060.81
2−0.060.410.820.010.050.980.010.060.97
30.060.760.860.020.080.990.070.690.88
4−0.071.280.87−0.101.240.87−0.122.180.70
50.021.310.930.021.260.940.032.270.81
60.061.690.95−0.031.380.970.032.370.88
70.021.750.970.001.380.99−0.042.530.93
80.092.650.960.061.790.990.062.890.94
90.113.920.920.052.110.990.083.610.94
100.064.310.930.042.290.99−0.023.660.96
110.074.920.940.072.930.990.115.210.92
12−0.3721.460.040.063.380.99−0.025.260.95
13−0.0421.670.06−0.125.190.97−0.116.780.91
140.2026.860.020.116.830.940.169.800.78
15−0.0026.860.03−0.047.020.96−0.049.970.82
16−0.0126.880.04−0.047.200.97−0.0210.030.87

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 (), so there was no obvious correlation and residual series was white noise.