An Optimized Fractional Grey Prediction Model for Carbon Dioxide Emissions Forecasting
Abstract
:1. Introduction
2. GM(1,1) and Fractional GM(1,1)
2.1. GM(1,1) Model
2.2. Fractional GM(1,1) Model
3. The Proposed Optimized Grey Prediction Model
3.1. Problem Formulation
3.2. Coding
3.3. Genetic Operations
3.3.1. Selection
3.3.2. Crossover and Mutation
3.3.3. Elitist Strategy
3.4. Algorithm Design
m←1; Generate nsize strings in Pm; //Initialization// while m < nmax do Compute the fitness value of each string in Pm; Choose the strings with top ndel fitness to be elites; repeat Randomly choose two strings from Pm; Put the string with higher fitness in the mating pool; until nsize strings in the mating pool; repeat Select the parent strings u and v from the mating pool; Perform crossover to generate new parameters; //Equations (17)–(19)// Add a tiny positive/negative value to each new parameter; //mutation// Add offspring u′ and v′ to Pm+1; until nsize strings in Pm+1; Randomly remove ndel strings from Pm+1; Add ndel elites to Pm+1; //elitist strategy// m←m + 1; end. |
4. Applications of CO2 Emissions Forecasting
4.1. Comparative Prediction Models
4.2. Experimental Results
5. Discussion
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Conflicts of Interest
References
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Country | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
China | 4068.1 | 4741.8 | 5407.5 | 5961.8 | 6473.2 | 6669.1 | 7131.5 | 7832.7 | 8570.9 | 8819.6 | 9190.5 | 9127.2 | 9101.4 | 9064.4 | 9257.9 |
USA | 5610.7 | 5688.8 | 5703.2 | 5602.4 | 5686.7 | 5512.5 | 5120.7 | 5352.1 | 5128.2 | 4903.0 | 5038.5 | 5046.6 | 4928.6 | 4838.5 | 4761.3 |
Russia | 1493.9 | 1488.2 | 1481.9 | 1537.7 | 1533.7 | 1553.8 | 1440.7 | 1529.2 | 1604.7 | 1607.9 | 1568.5 | 1551.6 | 1534.5 | 1510.6 | 1536.9 |
India | 950.3 | 1022.3 | 1073.7 | 1147.7 | 1260.9 | 1338.9 | 1502.3 | 1583.4 | 1667.8 | 1803.8 | 1854.8 | 2018.2 | 2026.7 | 2057.7 | 2161.6 |
Japan | 1174.4 | 1166.1 | 1166.8 | 1144.7 | 1186.4 | 1122.3 | 1070.3 | 1127.2 | 1183.5 | 1225.9 | 1234.0 | 1194.1 | 1155.7 | 1146.9 | 1132.4 |
Germany | 820.7 | 804.7 | 786.7 | 799.1 | 766.7 | 775.2 | 720.2 | 758.8 | 731.2 | 744.7 | 763.8 | 723.2 | 729.7 | 734.5 | 718.8 |
Canada | 534.3 | 526.2 | 540.4 | 531.1 | 561.9 | 541.9 | 514.4 | 528.6 | 541.2 | 539.7 | 549.6 | 555.5 | 557.7 | 548.1 | 547.8 |
Korea | 437.8 | 459.8 | 457.7 | 464.7 | 477.4 | 488.8 | 502.1 | 550.9 | 573.8 | 575.5 | 574.6 | 562.7 | 582.0 | 589.2 | 600.0 |
UK | 533.5 | 533.4 | 531.6 | 532.9 | 521.7 | 507.9 | 460.1 | 476.6 | 439.2 | 461.4 | 447.0 | 408.7 | 394.1 | 372.6 | 358.7 |
Iran | 357.4 | 385.9 | 417.8 | 449.3 | 480.1 | 487.3 | 504.3 | 498.6 | 507.8 | 512.3 | 536.0 | 556.7 | 553.3 | 554.4 | 567.1 |
Mexico | 386.6 | 396.0 | 412.4 | 426.9 | 433.4 | 434.5 | 425.2 | 440.5 | 456.5 | 459.5 | 449.6 | 434.2 | 442.4 | 446.2 | 446.0 |
Italy | 445.3 | 455.0 | 456.4 | 449.2 | 441.5 | 428.9 | 383.7 | 392.0 | 384.1 | 366.7 | 337.6 | 319.2 | 329.7 | 325.7 | 321.5 |
South Africa | 348.3 | 375.3 | 372.3 | 374.2 | 391.5 | 421.6 | 398.6 | 418.8 | 403.4 | 421.0 | 430.8 | 442.5 | 418.3 | 418.7 | 421.7 |
Saudi Arabia | 266.3 | 282.1 | 298.0 | 316.6 | 333.2 | 364.3 | 379.5 | 419.2 | 434.6 | 463.4 | 471.1 | 506.7 | 531.6 | 526.9 | 532.2 |
Australia | 348.0 | 361.3 | 365.5 | 370.8 | 381.1 | 384.3 | 391.1 | 383.6 | 382.1 | 381.7 | 375.8 | 367.0 | 373.8 | 381.9 | 384.6 |
Indonesia | 308.8 | 316.0 | 317.8 | 339.3 | 355.4 | 349.1 | 360.6 | 357.6 | 390.3 | 415.2 | 418.0 | 456.9 | 459.1 | 454.3 | 496.4 |
Brazil | 293.3 | 310.8 | 311.6 | 315.2 | 330.8 | 349.3 | 325.5 | 372.0 | 391.1 | 424.1 | 453.5 | 477.8 | 453.6 | 418.5 | 427.6 |
France | 368.3 | 369.1 | 371.9 | 362.6 | 353.8 | 349.5 | 336.1 | 340.2 | 322.3 | 325.3 | 325.3 | 293.2 | 299.6 | 301.7 | 306.1 |
Poland | 293.1 | 296.7 | 296.3 | 308.1 | 306.3 | 301.6 | 291.5 | 307.5 | 303.2 | 296.9 | 292.4 | 279.3 | 282.7 | 293.2 | 305.8 |
Spain | 302.6 | 319.3 | 333.7 | 325.0 | 337.9 | 309.8 | 276.1 | 262.1 | 264.9 | 260.5 | 235.2 | 232.1 | 247.1 | 237.4 | 253.4 |
Country | GM(1,1) | FAGM(1,1) | FANGBM(1,1) | FTDGM | NN | ARIMA | FTS | GA-FMGM(1,1) |
---|---|---|---|---|---|---|---|---|
China | 23.15 | 15.77 | 12.87 | 17.11 | 18.27 | 3.98 | 2.27 | 12.56 |
USA | 2.65 | 0.87 | 2.12 | 4.56 | 7.85 | 1.92 | 1.37 | 0.90 |
Russia | 5.42 | 2.70 | 3.42 | 7.98 | 7.56 | 0.76 | 1.01 | 0.71 |
India | 10.18 | 3.04 | 1.46 | 6.31 | 2.70 | 3.41 | 4.48 | 3.00 |
Japan | 4.52 | 22.63 | 15.17 | 13.43 | 13.03 | 0.90 | 2.82 | 2.31 |
Germany | 1.15 | 1.10 | 1.47 | 1.81 | 3.53 | 3.15 | 2.04 | 0.98 |
Canada | 1.72 | 3.17 | 2.14 | 3.58 | 1.55 | 2.57 | 0.78 | 1.06 |
Korea | 6.94 | 5.41 | 14.86 | 1.47 | 9.76 | 1.52 | 1.29 | 2.44 |
UK | 9.16 | 10.59 | 11.84 | 18.4 | 5.96 | 11.75 | 7.34 | 2.22 |
Iran | 4.09 | 4.45 | 5.9 | 5.86 | 1.27 | 4.72 | 1.94 | 0.96 |
Mexico | 7.44 | 3.45 | 2.7 | 4.49 | 5.34 | 1.31 | 2.86 | 1.02 |
Italy | 3.18 | 7.10 | 6.82 | 6.29 | 4.50 | 5.37 | 2.84 | 4.24 |
South Africa | 5.60 | 5.30 | 7 | 4.53 | 3.76 | 3.66 | 4.88 | 3.35 |
Saudi Arabia | 6.86 | 2.91 | 11.64 | 5.18 | 2.98 | 3.14 | 4.33 | 2.63 |
Australia | 3.55 | 3.06 | 2.85 | 1.98 | 2.03 | 1.75 | 1.71 | 1.70 |
Indonesia | 3.78 | 3.09 | 2.69 | 6.88 | 3.22 | 3.19 | 4.17 | 3.04 |
Brazil | 12.05 | 28.96 | 21.56 | 14.12 | 14.48 | 8.38 | 5.30 | 7.79 |
France | 3.37 | 3.84 | 4.44 | 12.93 | 3.34 | 4.35 | 3.80 | 3.02 |
Poland | 4.01 | 3.97 | 4.38 | 4.1 | 3.85 | 4.19 | 3.68 | 3.50 |
Spain | 8.34 | 14.33 | 13.01 | 13.48 | 9.40 | 5.63 | 4.94 | 4.02 |
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Hu, Y.-C.; Jiang, P.; Tsai, J.-F.; Yu, C.-Y. An Optimized Fractional Grey Prediction Model for Carbon Dioxide Emissions Forecasting. Int. J. Environ. Res. Public Health 2021, 18, 587. https://doi.org/10.3390/ijerph18020587
Hu Y-C, Jiang P, Tsai J-F, Yu C-Y. An Optimized Fractional Grey Prediction Model for Carbon Dioxide Emissions Forecasting. International Journal of Environmental Research and Public Health. 2021; 18(2):587. https://doi.org/10.3390/ijerph18020587
Chicago/Turabian StyleHu, Yi-Chung, Peng Jiang, Jung-Fa Tsai, and Ching-Ying Yu. 2021. "An Optimized Fractional Grey Prediction Model for Carbon Dioxide Emissions Forecasting" International Journal of Environmental Research and Public Health 18, no. 2: 587. https://doi.org/10.3390/ijerph18020587
APA StyleHu, Y. -C., Jiang, P., Tsai, J. -F., & Yu, C. -Y. (2021). An Optimized Fractional Grey Prediction Model for Carbon Dioxide Emissions Forecasting. International Journal of Environmental Research and Public Health, 18(2), 587. https://doi.org/10.3390/ijerph18020587