Submitted:
30 April 2025
Posted:
02 May 2025
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Abstract
Keywords:
Introduction and Literature Review
Methodology
















Results
Conclusion
References
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| Model | Stationary R-squared | R-squared | RMSE | MAPE | MAE | MaxAPE | MaxAE | Normalized BIC |
|---|---|---|---|---|---|---|---|---|
| I1.2021-Model_1 | 2.220E-16 | 2.220E-16 | 53512.539 | 410.551 | 37124.816 | 4001.255 | 146901.143 | 21.964 |
| I1.2022-Model_2 | 2.220E-16 | 2.220E-16 | 53373.319 | 473.371 | 37629.745 | 4896.578 | 146220.643 | 21.959 |
| I2.2021-Model_3 | 1.110E-16 | 1.110E-16 | 2855.529 | 475.876 | 2141.551 | 5238.903 | 6700.214 | 16.103 |
| I2.2022-Model_4 | 0.000 | 0.000 | 2870.759 | 526.423 | 2231.286 | 5937.255 | 6338.000 | 16.113 |
| I3.2021-Model_5 | 1.332E-15 | 1.332E-15 | 0.604 | 36.010 | 0.470 | 104.225 | 1.240 | -0.803 |
| I3.2022-Model_6 | 0.000 | 0.000 | 0.496 | 39.831 | 0.415 | 134.195 | 0.778 | -1.195 |
| I4.2021-Model_7 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | |||
| I4.2022-Model_8 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | |||
| I5.2021-Model_9 | 0.000 | 0.000 | 2575.481 | 776.120 | 1884.994 | 8324.615 | 6736.615 | 15.905 |
| I5.2022-Model_10 | 2.220E-16 | 2.220E-16 | 2713.581 | 694.858 | 2074.414 | 7469.636 | 6517.538 | 16.009 |
| I6.2021-Model_11 | 0.000 | 0.000 | 64.512 | 255.148 | 39.552 | 1185.203 | 182.705 | 8.552 |
| I6.2022-Model_12 | 0.000 | 0.000 | 61.427 | 516.093 | 37.934 | 4076.364 | 172.418 | 8.454 |
| I7.2021-Model_13 | 0.476 | 0.476 | 1401.245 | 184.267 | 1094.184 | 1102.151 | 2771.294 | 14.885 |
| I7.2022-Model_14 | 0.000 | 0.000 | 2035.800 | 643.814 | 1618.661 | 5505.981 | 4264.727 | 15.455 |
| I8.2021-Model_15 | 1.221E-15 | 1.221E-15 | 1.837 | 38.846 | 1.583 | 102.929 | 3.280 | 1.414 |
| I8.2022-Model_16 | 1.110E-15 | 1.110E-15 | 1.678 | 33.251 | 1.348 | 133.062 | 2.821 | 1.254 |
| I10.2021-Model_17 | 0.000 | 0.000 | 460.679 | 236.278 | 250.852 | 2070.085 | 1465.385 | 12.463 |
| I10.2022-Model_18 | 0.000 | 0.000 | 577.747 | 309.357 | 323.100 | 2052.778 | 1615.500 | 12.949 |
| I12.2021-Model_19 | 1.110E-15 | 1.110E-15 | 4.669 | 30.863 | 3.587 | 83.863 | 9.152 | 3.279 |
| I12.2022-Model_20 | -2.442E-15 | -2.442E-15 | 5.608 | 35.869 | 4.708 | 72.614 | 7.616 | 3.666 |
| I13.2021-Model_21 | 2.109E-15 | 2.109E-15 | 2.779 | 32.375 | 2.066 | 77.972 | 6.711 | 2.241 |
| I13.2022-Model_22 | 2.331E-15 | 2.331E-15 | 2.562 | 29.418 | 1.955 | 87.342 | 5.019 | 2.099 |
| I14.2021-Model_23 | -2.442E-15 | -2.442E-15 | 2.229 | 34.263 | 1.695 | 133.658 | 5.058 | 1.800 |
| I14.2022-Model_24 | 1.887E-15 | 1.887E-15 | 3.718 | 45.678 | 2.932 | 96.930 | 7.086 | 2.844 |
| I15.2021-Model_25 | 1.110E-16 | 1.110E-16 | 6.115 | 155.923 | 3.719 | 923.611 | 17.474 | 3.828 |
| I15.2022-Model_26 | 1.110E-16 | 1.110E-16 | 6.115 | 155.923 | 3.719 | 923.611 | 17.474 | 3.828 |
| I16.2021-Model_27 | -2.220E-16 | -2.220E-16 | 607177.035 | 959.081 | 437344.125 | 9633.142 | 1406132.250 | 26.840 |
| I16.2022-Model_28 | 1.110E-16 | 1.110E-16 | 612200.047 | 935.196 | 416188.611 | 9451.229 | 1437255.833 | 26.857 |
| I17.2021-Model_29 | 0.000 | 0.000 | 3482.545 | 669.528 | 2449.611 | 6957.778 | 8862.333 | 16.518 |
| I18.2021-Model_30 | 2.998E-15 | 2.998E-15 | 0.351 | 28.609 | 0.280 | 73.939 | 0.522 | -1.863 |
| I18.2022-Model_31 | -1.776E-15 | -1.776E-15 | 0.554 | 39.767 | 0.404 | 99.464 | 1.293 | -0.952 |
| I19.2021-Model_32 | 1.110E-16 | 1.110E-16 | 4467.195 | 1261.917 | 3012.132 | 11994.545 | 11455.909 | 17.027 |
| I19.2022-Model_33 | 0.000 | 0.000 | 6025.749 | 1847.049 | 3878.741 | 15663.492 | 14742.778 | 17.652 |
| I20.2021-Model_34 | 2.220E-16 | 2.220E-16 | 6316.157 | 433.367 | 3618.486 | 4141.012 | 18513.583 | 17.709 |
| I20.2022-Model_35 | -2.220E-16 | -2.220E-16 | 6300.247 | 1283.167 | 3617.181 | 14171.458 | 18519.417 | 17.704 |
| I21.2021-Model_36 | 0.000 | 0.000 | 3086.549 | 300.302 | 2089.514 | 2401.156 | 8141.417 | 16.277 |
| I21.2022-Model_37 | 0.000 | 0.000 | 3462.888 | 1027.351 | 2317.940 | 9131.842 | 8540.900 | 16.530 |
| I22.2021-Model_38 | 8.882E-16 | 8.882E-16 | 0.564 | 51.857 | 0.440 | 124.651 | 1.214 | -0.916 |
| I22.2022-Model_39 | -6.661E-16 | -6.661E-16 | 0.632 | 57.538 | 0.574 | 112.618 | 0.796 | -0.674 |
| I23.2021-Model_40 | 2.220E-15 | 2.220E-15 | 0.694 | 62.114 | 0.562 | 333.506 | 1.167 | -0.513 |
| I23.2022-Model_41 | 2.220E-16 | 2.220E-16 | 0.485 | 47.953 | 0.377 | 244.156 | 0.855 | -1.228 |
| I24.2021-Model_42 | -0.066 | 0.246 | 33.854 | 154.331 | 26.987 | 1233.983 | 55.603 | 7.251 |
| I24.2022-Model_43 | 0.852 | 0.325 | 28.859 | 79.821 | 23.509 | 552.470 | 44.761 | 7.139 |
| I25.2021-Model_44 | 1.110E-16 | 1.110E-16 | 576619.430 | 1079.848 | 436447.521 | 10025.736 | 1215095.455 | 26.748 |
| I25.2022-Model_45 | 0.000 | 0.000 | 582961.784 | 1026.026 | 413287.471 | 9548.053 | 1254080.545 | 26.770 |
| I26.2021-Model_46 | 0.000 | 0.000 | 2233.096 | 994.509 | 1785.320 | 8267.083 | 4796.900 | 15.653 |
| I27.2021-Model_47 | 2.220E-16 | 2.220E-16 | 2864.595 | 2724.302 | 2168.280 | 23404.000 | 5503.600 | 16.151 |
| I27.2022-Model_48 | 0.000 | 0.000 | 3191.451 | 1859.566 | 2017.407 | 14456.349 | 8133.111 | 16.381 |
| I28.2021-Model_49 | 1.998E-15 | 1.998E-15 | 22.674 | 73.220 | 18.276 | 297.552 | 34.278 | 6.473 |
| I28.2022-Model_50 | -4.441E-16 | -4.441E-16 | 23.652 | 89.175 | 20.986 | 278.498 | 32.083 | 6.557 |
| Arima Model Parameters | |||||
|---|---|---|---|---|---|
| Model | Transformation | Estimate | SE | t | Sig. |
| I1.2021-Model_1 | Constant | 48558.857 | 14301.828 | 3.395 | 0.005 |
| I1.2022-Model_2 | Constant | 49116.357 | 14264.620 | 3.443 | 0.004 |
| I2.2021-Model_3 | Constant | 2989.786 | 763.172 | 3.918 | 0.002 |
| I2.2022-Model_4 | Constant | 3079.000 | 767.243 | 4.013 | 0.001 |
| I3.2021-Model_5 | Constant | 1.450 | 0.174 | 8.323 | 0.000 |
| I3.2022-Model_6 | Constant | 1.358 | 0.143 | 9.486 | 0.000 |
| I4.2021-Model_7 | Constant | 1.000 | 0.000 | ||
| I4.2022-Model_8 | Constant | 1.000 | 0.000 | ||
| I5.2021-Model_9 | Constant | 2527.385 | 714.310 | 3.538 | 0.004 |
| I5.2022-Model_10 | Constant | 2876.462 | 752.612 | 3.822 | 0.002 |
| I6.2021-Model_11 | Constant | 47.295 | 19.451 | 2.431 | 0.035 |
| I6.2022-Model_12 | Constant | 43.852 | 18.521 | 2.368 | 0.039 |
| I7.2021-Model_13 | Constant | 2072.089 | 235.791 | 8.788 | 0.000 |
| AR | -0.703 | 0.214 | -3.290 | 0.007 | |
| I7.2022-Model_14 | Constant | 2130.273 | 613.817 | 3.471 | 0.006 |
| I8.2021-Model_15 | Constant | 4.850 | 0.510 | 9.519 | 0.000 |
| I8.2022-Model_16 | Constant | 4.941 | 0.506 | 9.763 | 0.000 |
| I10.2021-Model_17 | Constant | 390.615 | 127.769 | 3.057 | 0.010 |
| I10.2022-Model_18 | Constant | 387.500 | 182.700 | 2.121 | 0.063 |
| I12.2021-Model_19 | Constant | 13.348 | 1.295 | 10.309 | 0.000 |
| I12.2022-Model_20 | Constant | 15.294 | 1.691 | 9.045 | 0.000 |
| I13.2021-Model_21 | Constant | 7.439 | 0.771 | 9.652 | 0.000 |
| I13.2022-Model_22 | Constant | 7.831 | 0.772 | 10.139 | 0.000 |
| I14.2021-Model_23 | Constant | 5.912 | 0.618 | 9.563 | 0.000 |
| I14.2022-Model_24 | Constant | 7.464 | 1.121 | 6.659 | 0.000 |
| I15.2021-Model_25 | Constant | 0.494 | 1.765 | 0.280 | 0.785 |
| I15.2022-Model_26 | Constant | 0.494 | 1.765 | 0.280 | 0.785 |
| I16.2021-Model_27 | Constant | 573184.750 | 175277.023 | 3.270 | 0.007 |
| I16.2022-Model_28 | Constant | 560657.167 | 176726.991 | 3.172 | 0.009 |
| I17.2021-Model_29 | Constant | 4234.667 | 1005.324 | 4.212 | 0.001 |
| I18.2021-Model_30 | Constant | 1.148 | 0.111 | 10.338 | 0.000 |
| I18.2022-Model_31 | Constant | 1.117 | 0.175 | 6.378 | 0.000 |
| I19.2021-Model_32 | Constant | 4233.091 | 1346.910 | 3.143 | 0.010 |
| I19.2022-Model_33 | Constant | 5517.222 | 2008.583 | 2.747 | 0.025 |
| I20.2021-Model_34 | Constant | 5937.417 | 1823.317 | 3.256 | 0.008 |
| I20.2022-Model_35 | Constant | 5708.583 | 1818.725 | 3.139 | 0.009 |
| I21.2021-Model_36 | Constant | 3426.583 | 891.010 | 3.846 | 0.003 |
| I21.2022-Model_37 | Constant | 3508.100 | 1095.061 | 3.204 | 0.011 |
| I22.2021-Model_38 | Constant | 0.966 | 0.178 | 5.417 | 0.000 |
| I22.2022-Model_39 | Constant | 1.254 | 0.211 | 5.956 | 0.000 |
| I23.2021-Model_40 | Constant | 1.517 | 0.209 | 7.252 | 0.000 |
| I23.2022-Model_41 | Constant | 1.205 | 0.146 | 8.232 | 0.000 |
| I25.2021-Model_44 | Constant | 530588.545 | 173857.374 | 3.052 | 0.012 |
| I25.2022-Model_45 | Constant | 515495.455 | 175769.564 | 2.933 | 0.015 |
| I26.2021-Model_46 | Constant | 2008.100 | 706.167 | 2.844 | 0.019 |
| I27.2021-Model_47 | Constant | 2350.400 | 905.865 | 2.595 | 0.029 |
| I27.2022-Model_48 | Constant | 2037.889 | 1063.817 | 1.916 | 0.092 |
| I28.2021-Model_49 | Constant | 45.798 | 7.170 | 6.387 | 0.000 |
| I28.2022-Model_50 | Constant | 43.603 | 7.479 | 5.830 | 0.000 |
| Exponential Smoothing Model Parameters | |||||
| Model | Transformation | Estimate | SE | t | Sig. |
| I24.2021-Model_42 | Alpha (Level) | 0.731 | 0.287 | 2.545 | 0.027 |
| I24.2022-Model_43 | Alpha (Level) | 0.100 | 0.104 | 0.963 | 0.358 |
| Gamma (Trend) | 2.336E-05 | 0.129 | 0.000 | 1.000 | |
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