The Role of GARCH Effect on the Prediction of Air Pollution
Abstract
:1. Introduction
2. Materials and Methods
2.1. Literature Review
2.2. Dataset
2.3. Methodology
2.3.1. Unit Root Test
- Model with neither intercept nor trend
- 2.
- Model with intercept but without trend
- 3.
- Model with both intercept and trend
2.3.2. ARCH Test
2.3.3. GARCH Model
2.3.4. GA-SVM Model
2.3.5. Evaluation Indicators for Prediction Models
3. Results and Discussion
3.1. GARCH Effect Diagnosis
3.2. GARCH Estimation
3.3. Evaluations of the Prediction Models
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Station 1 | Station 2 | Station 3 | Station 4 | Station 5 | |
---|---|---|---|---|---|
Location | FongYen | SaLu | DaLi | ChungMin | SeaTun |
Duration | 58 days | 58 days | 58 days | 58 days | 58 days |
Frequency | Hourly | Hourly | Hourly | Hourly | Hourly |
Observations | 1211 | 1211 | 1215 | 1211 | 1211 |
Mean absolute percentage error (MAPE) | |
Root mean squared error (RMSE) | |
Mean absolute error (MAE) | |
Correlation coefficient (C. C.) | Here, is the mean value over the test data. |
MAPE | Intepretation |
---|---|
MAPE < 10% | Highly accurate forecasting |
10% <MAPE < 20% | Good forecasting |
20% <MAPE < 50% | Reasonable forecasting |
50% <MAPE | Inaccuracte forecasting |
Variable | Station 1 | Station 2 | Station 3 | Station 4 | Station 5 |
---|---|---|---|---|---|
PM2.5 (t−1) | 0.5408 | 0.5828 | 0.4945 | 0.5563 | 0.5543 |
25.80 *** | 31.70 *** | 24.83 *** | 30.10 *** | 28.47 *** | |
CO | −0.9842 | 0.5406 | −0.1548 | −0.2233 | 0.9440 |
−1.94 | 1.14 | −0.47 | −0.51 | 1.70 | |
NO | 1.2822 | −0.0410 | −0.0046 | 0.2324 | 0.2220 |
1.55 | −0.56 | −0.01 | 0.47 | 0.34 | |
NO2 | 1.2568 | 0.1181 | −0.1277 | 0.2902 | 0.1788 |
1.54 | 2.19 ** | −0.23 | 0.59 | 0.27 | |
NOX | −1.0688 | −0.0139 | 0.1713 | −0.2036 | −0.1715 |
−1.31 | −0.31 | 0.30 | −0.42 | −0.26 | |
O3 | −0.0102 | 0.0090 | 0.0068 | 0.0030 | 0.0016 |
−0.82 | 0.75 | 0.51 | 0.25 | 0.13 | |
PM10 | 0.1547 | 0.1734 | 0.1970 | 0.1927 | 0.1801 |
13.28 *** | 16.86 *** | 18.01 *** | 17.60 *** | 16.73 *** | |
SO2 | 0.4612 | 0.5779 | 0.6934 | 0.5627 | 0.3856 |
9.84 *** | 9.84 *** | 11.05 *** | 8.72 *** | 6.07 *** | |
WindDirection | 0.0004 | 0.0012 | 0.0019 | −0.0003 | −0.0026 |
0.30 | 1.30 | 1.82 | −0.42 | −2.52 ** | |
WindSpeed | 0.3763 | −0.1501 | −0.0007 | −0.4826 | −0.5618 |
−2.15 ** | −1.86* | −0.09 | −3.14 *** | −5.11 *** | |
C | 0.8794 | −1.3351 | −1.2469 | −0.1998 | 2.0251 |
1.71 * | −2.75 *** | −3.56 *** | −0.39 | 3.43 *** | |
Observation | 1211 | 1211 | 1215 | 1211 | 1211 |
F-statistic | 423.2258 | 739.5768 | 710.4244 | 740.6729 | 602.5055 |
Prob. (F-stat.) | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |
Adj. R2 | 0.7773 | 0.8592 | 0.8532 | 0.8594 | 0.8325 |
LM Test | |||||
F-statistic | 16.2423 | 20.4623 | 21.2019 | 21.6132 | 20.8101 |
Prob. (F-stat.) | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |
Obs*R2 | 31.9702 | 40.0022 | 41.4075 | 42.17369 | 40.6592 |
Prob. (Chi2) | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |
ARCH test | |||||
F-statistic | 231.4378 | 24.6600 | 31.1825 | 96.8117 | 148.2826 |
Prob. (F-stat.) | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |
Obs*R2 | 194.5480 | 24.2067 | 30.4505 | 89.7771 | 132.2895 |
Prob. (Chi2) | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |
Variable | Station 1 | Station 2 | Station 3 | Station 4 | Station 5 |
---|---|---|---|---|---|
GARCH (1,1) | |||||
PM2.5 (t−1) | 0.5210 | 0.5528 | 0.4402 | 0.5577 | 0.4786 |
27.31 *** | 33.80 *** | 31.17 *** | 41.47 *** | 28.22 *** | |
CO | 2.9016 | 2.4174 | 0.5319 | 2.5439 | 3.3907 |
6.28 *** | 8.16 *** | 1.47 | 9.13 *** | 5.75 *** | |
NO | 0.9557 | −0.0513 | 0.6952 | 0.1474 | 0.1618 |
1.38 | −0.34 | 2.68 *** | 0.36 | 0.21 | |
NO2 | 1.0488 | 0.0779 | 0.5710 | 0.1766 | 0.1172 |
1.53 | 0.53 | 2.24 ** | 0.44 | 0.16 | |
NOx | −0.9170 | −0.0024 | −0.5645 | −0.1312 | -0.1266 |
−1.33 | −0.02 | −2.21 ** | −0.32 | -0.17 | |
O3 | −0.0025 | −0.0064 | −0.0153 | 0.0064 | 0.0060 |
−0.28 | −0.64 | −1.26 | 0.75 | 0.58 | |
PM10 | 0.1634 | 0.1635 | 0.2327 | 0.1755 | 0.2001 |
18.24 *** | 26.84 *** | 31.04 *** | 29.07 *** | 26.42 *** | |
SO2 | 0.2115 | 0.5537 | 0.6148 | 0.2355 | 0.2485 |
5.64 *** | 16.23 *** | 9.04 *** | 5.42 *** | 3.71 *** | |
WindDirection | −0.0012 | −0.0006 | −0.0001 | −0.0002 | −0.0024 |
−1.28 | −0.95 | −0.10 | −0.28 | −3.40 *** | |
WindSpeed | −0.3804 | −0.2110 | 0.0008 | −0.2507 | −0.4646 |
−2.73 *** | −3.40 *** | 0.07 | −2.02 ** | −5.44 *** | |
C | 1.1559 | −0.6811 | −0.4225 | −0.0385 | 1.8648 |
2.76 *** | −1.66 * | −1.69 * | −0.10 | 4.10 *** | |
Variance Equation | |||||
2.8001 | 0.5845 | 7.1652 | 1.3838 | 0.9128 | |
C | 7.03 *** | 6.24 *** | 9.53 *** | 5.47 *** | 4.01 *** |
0.3133 | 0.1689 | 0.4319 | 0.2426 | 0.1741 | |
ε2(t−1) | 8.81 *** | 8.53 *** | 10.44 *** | 8.46 *** | 10.03 *** |
0.5639 | 0.8122 | 0.2937 | 0.6820 | 0.7891 | |
h(t−1) | 14.08 *** | 44.93 *** | 5.72 *** | 20.11 *** | 35.78 *** |
Model | Station 1 | Station 2 | Station 3 | Station 4 | Station 5 |
---|---|---|---|---|---|
SVM | |||||
MAPE | 10.33% | 35.94% | 21.64% | 26.89% | 16.08% |
RMSE | 3.9405 | 4.7224 | 2.9855 | 7.2913 | 4.2309 |
GA-SVM | |||||
MAPE | 10.42% | 33.14% | 25.72% | 26.64% | 15.88% |
RMSE | 4.0778 | 4.4938 | 3.1561 | 7.3327 | 4.2144 |
GA-SVM-GARCH | |||||
MAPE | 0.32% | 0.68% | 0.61% | 0.14% | 0.14% |
RMSE | 0.0596 | 0.0950 | 0.0632 | 0.0313 | 0.0255 |
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Yao, K.-C.; Hsueh, H.-W.; Huang, M.-H.; Wu, T.-C. The Role of GARCH Effect on the Prediction of Air Pollution. Sustainability 2022, 14, 4459. https://doi.org/10.3390/su14084459
Yao K-C, Hsueh H-W, Huang M-H, Wu T-C. The Role of GARCH Effect on the Prediction of Air Pollution. Sustainability. 2022; 14(8):4459. https://doi.org/10.3390/su14084459
Chicago/Turabian StyleYao, Kai-Chao, Hsiu-Wen Hsueh, Ming-Hsiang Huang, and Tsung-Che Wu. 2022. "The Role of GARCH Effect on the Prediction of Air Pollution" Sustainability 14, no. 8: 4459. https://doi.org/10.3390/su14084459