Evaluation of the Models for Forecasting Dengue in Brazil from 2000 to 2017: An Ecological Time-Series Study
Abstract
:Simple Summary
Abstract
1. Introduction
2. Materials and Methods
2.1. Design
2.2. Study Sites
2.3. Data Source
2.4. Variables
2.5. Data Analysis and Statistical Modeling
- (1)
- Mean absolute percentage error (MAPE), in which the absolute difference (At − Ft) represents the distance between the actual value At and the estimated value Ft in the forecast. The ratio of the distance (At − Ft) to the actual value At was multiplied by 100% to obtain the percentage distance. The sum of the percentage error calculated for each month of the time series was divided by the number of months to obtain the average percentage distance according to the formula given below:
- (2)
- Relative MAPE scale, in which the MAPE of the null model is divided by the MAPE value of each model. If the result of this division is ≤1, the model is classified as having poor predictive accuracy. If the value is >1 and ≤2, the model is classified as having low predictive accuracy. A relative MAPE value >2 means that the model possesses reliable predictive accuracy.
- (3)
- Coefficient of uncertainty (Theil’s U) measures the relative accuracy by penalizing statistical models with high deviations from the mean value. Values <1 represent reliable predictive capability [27].
3. Results
4. Discussion
5. Conclusions
Supplementary Materials
Author Contributions
Funding
Conflicts of Interest
References
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Brazilian States and the Federal District | Total Jan. 2000–Dec. 2017 | Monthly Average (Standard Deviation) n = 216 | Median Monthly n = 216 | Minimum Monthly n = 216 | Maximum Monthly n = 216 | Test of Stationariness n = 216 |
---|---|---|---|---|---|---|
Acre | 209,830 | 971 (1764) | 323 | 6 | 10,653 | Yes |
Alagoas | 272,832 | 1263 (1704) | 611 | 22 | 10,818 | Yes |
Amazonas | 210,506 | 975 (2395) | 437 | 13 | 22,319 | Yes |
Amapá | 58,500 | 271 (264) | 187 | 0 | 1881 | Yes |
Bahia | 894,494 | 4141 (6005) | 1632 | 67 | 41,277 | Yes |
Ceará | 975,734 | 4517 (5414) | 2525 | 66 | 29,665 | Yes |
Distrito Federal | 141,632 | 656 (1179) | 216 | 7 | 6802 | Yes |
Espírito Santo | 560,814 | 2596 (3365) | 1329 | 67 | 18,937 | Yes |
Goiás | 1,152,397 | 5335 (8135) | 2191 | 51 | 40,608 | Yes |
Maranhão | 168,909 | 782 (1018) | 470 | 28 | 7986 | Yes |
Minas Gerais | 2,385,230 | 11,043 (27,958) | 2565 | 8 | 202,922 | Yes |
Mato Grosso do Sul | 512,062 | 2371 (5033) | 551 | 1 | 27,348 | Yes |
Mato Grosso | 393,688 | 1823 (2584) | 828 | 0 | 16,566 | Yes |
Pará | 303,257 | 1404 (1270) | 890 | 225 | 6812 | Yes |
Paraíba | 235,798 | 1092 (1616) | 470 | 0 | 12,189 | Yes |
Pernambuco | 822,514 | 3808 (6554) | 1442 | 193 | 41,966 | Yes |
Piauí | 167,531 | 776 (782) | 481 | 21 | 4714 | Yes |
Paraná | 720,436 | 3335 (6170) | 1164 | 15 | 37,914 | Yes |
Rio de Janeiro | 1,696,598 | 7855 (16,823) | 1684 | 32 | 100,762 | Yes |
Rio Grande do Norte | 400,889 | 1856 (2665) | 928 | 71 | 21,847 | Yes |
Rondônia | 161,992 | 750 (1322) | 336 | 9 | 11,556 | Yes |
Roraima | 84,386 | 391 (358) | 269 | 53 | 2480 | Yes |
Rio Grande do Sul | 29,192 | 135 (339) | 34 | 1 | 2621 | Yes |
Santa Catarina | 35,900 | 166 (532) | 35 | 2 | 4768 | Yes |
Sergipe | 125,160 | 579 (1431) | 233 | 22 | 17,612 | Yes |
São Paulo | 3,687,743 | 17,073 (37,676) | 4976 | 262 | 322,982 | Yes |
Tocantins | 246,316 | 1140 (1194) | 699 | 29 | 5730 | Yes |
Brazilian States and the Federal District | Reliable Models (12-Month Forecasting Horizon) | Reliable Models (6-Month Forecasting Horizon) | Reliable Models (3-Month Forecasting Horizon) |
---|---|---|---|
Acre | ELM, BATS | TBATS, NNETAR, BATS | BATS, TBATS, ETS |
Alagoas | - | - | ARIMA |
Amazonas | - | - | ELM, MLP |
Amapá | - | ETS, TBATS, STLM | ETS, StructTS |
Bahia | - | StructTS | ELM |
Ceará | NNETAR, ARIMA | ARIMA | - |
Distrito Federal | STLM | - | - |
Espírito Santo | - | - | MLP |
Goiás | - | - | MLP |
Maranhão | ARIMA, TBATS, ETS | STLM, TBATS, ARIMA | ETS, BATS, ARIMA |
Minas Gerais | - | - | - |
Mato Grosso do Sul | - | - | - |
Mato Grosso | ARIMA, ETS | - | - |
Pará | STLM | - | - |
Paraíba | - | - | - |
Pernambuco | - | - | ELM, StrucTS, STLM |
Piauí | ARIMA, STLM, BATS | TBATS, BATS | StructTS |
Paraná | - | ARIMA | ELM, MLP |
Rio de Janeiro | - | - | - |
Rio Grande do Norte | - | StructTS | StructTS |
Rondônia | - | - | ELM |
Roraima | - | - | - |
Rio Grande do Sul | - | - | - |
Santa Catarina | - | - | ARIMA |
Sergipe | - | ETS, STLM | - |
São Paulo | - | - | - |
Tocantins | - | - | - |
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Lima, M.V.M.d.; Laporta, G.Z. Evaluation of the Models for Forecasting Dengue in Brazil from 2000 to 2017: An Ecological Time-Series Study. Insects 2020, 11, 794. https://doi.org/10.3390/insects11110794
Lima MVMd, Laporta GZ. Evaluation of the Models for Forecasting Dengue in Brazil from 2000 to 2017: An Ecological Time-Series Study. Insects. 2020; 11(11):794. https://doi.org/10.3390/insects11110794
Chicago/Turabian StyleLima, Marcos Venícius Malveira de, and Gabriel Zorello Laporta. 2020. "Evaluation of the Models for Forecasting Dengue in Brazil from 2000 to 2017: An Ecological Time-Series Study" Insects 11, no. 11: 794. https://doi.org/10.3390/insects11110794