Functional Location-Scale Model to Forecast Bivariate Pollution Episodes
Abstract
:1. Introduction
2. Methodology
2.1. Mathematical Model
2.2. Estimation Algorithm
3. Case Study: Joint Forecasting of Pollution Episodes
4. Discussion
Author Contributions
Acknowledgments
Conflicts of Interest
References
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Model | ||||||||
M | X | X | ||||||
M | X | X | X | X | ||||
M | X | X | X | X | ||||
M | X | X | X | X | X | X | X |
K | M | M | M | M | |||
0.50 | 10 | 20 | 3 | 0.43 | 0.47 | 0.45 | 0.51 |
5 | 0.42 | 0.48 | 0.47 | 0.49 | |||
10 | 49 | 3 | 0.51 | 0.52 | 0.52 | 0.52 | |
5 | 0.51 | 0.50 | 0.50 | 0.50 | |||
20 | 20 | 3 | 0.45 | 0.49 | 0.44 | 0.49 | |
5 | 0.48 | 0.46 | 0.43 | 0.46 | |||
20 | 49 | 3 | 0.50 | 0.54 | 0.51 | 0.50 | |
5 | 0.49 | 0.49 | 0.49 | 0.48 | |||
0.75 | 10 | 20 | 3 | 0.70 | 0.73 | 0.72 | 0.75 |
5 | 0.69 | 0.74 | 0.73 | 0.74 | |||
10 | 49 | 3 | 0.76 | 0.78 | 0.78 | 0.78 | |
5 | 0.77 | 0.76 | 0.76 | 0.76 | |||
20 | 20 | 3 | 0.70 | 0.72 | 0.70 | 0.72 | |
5 | 0.70 | 0.71 | 0.69 | 0.69 | |||
20 | 49 | 3 | 0.77 | 0.78 | 0.75 | 0.73 | |
5 | 0.75 | 0.74 | 0.72 | 0.72 | |||
0.90 | 10 | 20 | 3 | 0.88 | 0.87 | 0.87 | 0.89 |
5 | 0.86 | 0.88 | 0.87 | 0.88 | |||
10 | 49 | 3 | 0.91 | 0.90 | 0.90 | 0.90 | |
5 | 0.90 | 0.90 | 0.90 | 0.90 | |||
20 | 20 | 3 | 0.87 | 0.87 | 0.85 | 0.86 | |
5 | 0.87 | 0.86 | 0.86 | 0.84 | |||
20 | 49 | 3 | 0.90 | 0.89 | 0.90 | 0.86 | |
5 | 0.87 | 0.87 | 0.88 | 0.85 | |||
0.95 | 10 | 20 | 3 | 0.93 | 0.93 | 0.93 | 0.93 |
5 | 0.93 | 0.93 | 0.93 | 0.93 | |||
10 | 49 | 3 | 0.96 | 0.93 | 0.93 | 0.93 | |
5 | 0.95 | 0.94 | 0.94 | 0.94 | |||
20 | 20 | 3 | 0.93 | 0.93 | 0.92 | 0.92 | |
5 | 0.92 | 0.92 | 0.93 | 0.90 | |||
20 | 49 | 3 | 0.95 | 0.94 | 0.95 | 0.92 | |
5 | 0.92 | 0.92 | 0.93 | 0.90 |
Episode 1 | Episode 2 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Repsonse | K | M | M | M | M | M | M | M | M | ||
NO | 10 | 20 | 3 | 20.7 | 25.2 | 20.0 | 23.0 | 1.9 | 1.7 | 1.4 | 1.4 |
5 | 19.6 | 18.6 | 20.6 | 16.4 | 0.9 | 0.8 | 0.8 | 0.6 | |||
49 | 3 | 20.9 | 24.7 | 18.2 | 23.8 | 1.8 | 1.9 | 1.4 | 1.4 | ||
5 | 19.2 | 17.5 | 19.3 | 16.7 | 0.9 | 0.9 | 0.8 | 0.7 | |||
20 | 100 | 3 | 34.0 | 24.7 | 19.9 | 19.6 | 3.3 | 5.5 | 1.7 | 3.1 | |
5 | 40.9 | 23.3 | 46.5 | 29.2 | 1.5 | 2.5 | 1.0 | 1.8 | |||
49 | 3 | 30.2 | 18.2 | 18.7 | 20.4 | 3.4 | 5.3 | 1.7 | 2.8 | ||
5 | 36.2 | 27.6 | 39.8 | 35.6 | 1.5 | 2.5 | 1.0 | 1.8 | |||
SO | 10 | 100 | 3 | 505.0 | 841.0 | 407.5 | 837.3 | 544.8 | 531.9 | 419.8 | 419.1 |
5 | 914.9 | 868.6 | 669.4 | 516.3 | 215.6 | 230.3 | 184.5 | 199.1 | |||
49 | 3 | 686.0 | 685.3 | 515.8 | 518.3 | 481.4 | 484.4 | 338.0 | 361.1 | ||
5 | 991.1 | 925.5 | 846.3 | 682.9 | 199.9 | 214.7 | 170.6 | 179.9 | |||
20 | 100 | 3 | 1463.4 | 2172.7 | 825.4 | 1199.9 | 1154.5 | 1133.1 | 709.5 | 659.0 | |
5 | 1470.6 | 2531.2 | 1002.9 | 1428.5 | 525.5 | 482.1 | 352.0 | 341.3 | |||
49 | 3 | 1.458.7 | 2485.4 | 768.4 | 698.4 | 1162.6 | 1125.8 | 644.8 | 628.7 | ||
5 | 1787.6 | 2811.0 | 1111.2 | 951.5 | 548.1 | 492.0 | 352.7 | 359.3 |
Memory (MB) | Runtime (seconds) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
K | M | M | M | M | M | M | M | M | ||
10 | 20 | 3 | 652.70 | 1083.03 | 1319.57 | 2266.34 | 17.98 | 29.66 | 35.99 | 61.62 |
5 | 1090.78 | 1855.39 | 2299.14 | 4075.88 | 35.55 | 55.29 | 63.15 | 124.7 | ||
49 | 3 | 329.94 | 548.58 | 669.42 | 1153.38 | 10.53 | 17.42 | 21.38 | 37.01 | |
5 | 552.74 | 942.68 | 1171.67 | 2089.53 | 19.79 | 31.28 | 46.62 | 88.20 | ||
20 | 20 | 3 | 653.34 | 1084.15 | 1320.66 | 2268.16 | 18.11 | 29.63 | 35.97 | 61.21 |
5 | 1091.90 | 1857.26 | 2300.99 | 4078.95 | 32.14 | 49.51 | 72.45 | 124.81 | ||
49 | 3 | 330.10 | 548.84 | 669.69 | 1153.82 | 10.51 | 17.56 | 21.49 | 37.82 | |
5 | 553.01 | 943.13 | 1172.20 | 2090.36 | 17.80 | 36.44 | 39.03 | 76.11 |
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Oviedo-de La Fuente, M.; Ordóñez, C.; Roca-Pardiñas, J. Functional Location-Scale Model to Forecast Bivariate Pollution Episodes. Mathematics 2020, 8, 941. https://doi.org/10.3390/math8060941
Oviedo-de La Fuente M, Ordóñez C, Roca-Pardiñas J. Functional Location-Scale Model to Forecast Bivariate Pollution Episodes. Mathematics. 2020; 8(6):941. https://doi.org/10.3390/math8060941
Chicago/Turabian StyleOviedo-de La Fuente, Manuel, Celestino Ordóñez, and Javier Roca-Pardiñas. 2020. "Functional Location-Scale Model to Forecast Bivariate Pollution Episodes" Mathematics 8, no. 6: 941. https://doi.org/10.3390/math8060941
APA StyleOviedo-de La Fuente, M., Ordóñez, C., & Roca-Pardiñas, J. (2020). Functional Location-Scale Model to Forecast Bivariate Pollution Episodes. Mathematics, 8(6), 941. https://doi.org/10.3390/math8060941