Table 1 Comparison of ARIMA model and hybrid model predictive value PE
type of data | CASE (The amount of data, the amount of observation set) & ARIMA(p,d,q) | ARIMA forecasting | ARIMA and adaptive combination forecasting | Number of iterations | Iteration time (s) | ||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
PEmax (%) | PEmin(%) | MAPE(%) | σ PE(%) | PEmax (%) | PEmin (%) | MAPE(%) | σ PE(%) | ||||
Stationarity | Case 1 (348,336) ARIMA(3, 0, 3) | 106.73 | 0.34 | 38.4 | 29.2 | 0.67 | 0.00 | 0.101 | 0.199 | 666 | 2.28 |
Case 2 (384,372) ARIMA(2, 0, 5) | 134.71 | 3.25 | 40.91 | 35.6 | 0.62 | 0.07 | 0.14 | 0.19 | 2208 | 3 | |
Case 3 (852,840) ARIMA(7, 0, 7) | 49.9 | 1.8 | 15.2 | 13.9 | 0.192 | 0.003 | 0.05 | 0.06 | 1670 | 5 | |
Cyclical and trending | Case 4 (168,156) ARIMA(5, 1, 5) | 11.0 | 0.1 | 3.1 | 2.9 | 0.08 | 0.01 | 0.02 | 0.02 | 13,892 | 7 |
Case 5 (476,464) ARIMA(6, 1, 4) | 8.25 | 0.36 | 4.67 | 0.23 | 1.29 | 0.002 | 0.42 | 0.47 | 30,492 | 10 | |
Case 6 (252,240) ARIMA(5, 1, 5) | 19.5 | 1.33 | 9.1 | 6.01 | 2.4 | 0.0003 | 0.41 | 0.74 | 1410 | 5 | |
Case 7 (178,168) ARIMA(5, 1, 5) | 3.63 | 0.33 | 1.8 | 1.15 | 1.266 | 0.0002 | 0.509 | 0.523 | 14,507 | 13 | |
Upward trend | Case 8 (82,77) ARIMA(4, 1, 4) | 13.59 | 2.34 | 7.33 | 3.88 | 0.005 | 0.004 | 0.005 | 0.001 | 803 | 3.9 |
Case 9 (418,406) ARIMA(3, 1, 6) | 3.58 | 0.17 | 1.2 | 0.91 | 0.103 | 0.003 | 0.052 | 0.029 | 8932 | 6.8 | |
Case 10 (43,38) ARIMA(1, 1, 3) | 10.62 | 6.95 | 8.5 | 1.24 | 8.13 | 0.07 | 1.8 | 3.18 | 2805 | 4 | |
Downward trend | Case 11 (304,296) ARIMA(6, 1, 6) | 16.81 | 2.94 | 9.78 | 5.29 | 1.204 | 0.002 | 0.39 | 0.39 | 13,050 | 10 |
Case 12 (102,92) ARIMA(1, 0, 0) | 4.83 | 0.36 | 2.6 | 1.62 | 3.62 | 0.21 | 1.7 | 0.99 | 6622 | 3.054 | |
Case 13 (65,55) ARIMA(3, 1, 3) | 6.89 | 1.08 | 4.46 | 1.6 | 5.9 | 0.64 | 3.89 | 1.77 | 4017 | 3 | |