Table 2.
Results of the correlation coefficients of Pearson, Spearman, and Kendall, and of the RMSE% for the ARIMA models built for Brazil and its 27 federative units.
| State | Model | Pearson | Spearman | Kendall | RMSE | RMSE (%) | MAPE | MPE | MAE | ME | Number of observations |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Acre | ARIMA(2,2,0) | 0.99890 | 0.99515 | 0.96645 | 9.30 | 4.78 | 7.50 | 1.48 | 6.34 | 1.56 | 50 |
| Alagoas | ARIMA(0,2,1) | 0.99873 | 0.99371 | 0.96337 | 22.21 | 5.13 | 6.93 | 2.36 | 10.83 | 2.50 | 59 |
| Amazonas | ARIMA(0,2,1) | 0.99928 | 0.99899 | 0.99194 | 87.65 | 4.10 | 6.56 | 3.77 | 54.04 | 20.92 | 54 |
| Amapá | ARIMA(0,2,1) | 0.99647 | 0.99826 | 0.98327 | 43.04 | 8.78 | 10.59 | 3.77 | 21.64 | 8.31 | 47 |
| Bahia | ARIMA(2,2,1) | 0.99971 | 0.99892 | 0.98795 | 28.59 | 2.56 | 7.78 | 1.30 | 18.40 | 7.36 | 61 |
| Ceará | ARIMA(0,2,1) | 0.99408 | 1.00000 | 1.00000 | 351.5 | 11.31 | 5.69 | 4.65 | 122.61 | 75.44 | 51 |
| Distrito Federal | ARIMA(0,2,1) | 0.99922 | 0.99937 | 0.99151 | 20.70 | 4.02 | 7.00 | 3.56 | 14.29 | 3.87 | 60 |
| Espírito Santo | ARIMA(0,2,1) | 0.99874 | 0.99870 | 0.98565 | 51.50 | 5.09 | 7.82 | 3.70 | 26.9 | 8.60 | 62 |
| Goiás | ARIMA(0,2,1) | 0.99884 | 0.99971 | 0.99596 | 13.55 | 4.91 | 5.50 | 2.62 | 8.54 | 2.67 | 55 |
| Maranhão | ARIMA(0,2,0) | 0.99908 | 0.99867 | 0.98841 | 63.78 | 4.42 | 10.00 | 1.20 | 41.77 | 10.57 | 47 |
| Minas Gerais | ARIMA(1,2,2) | 0.99945 | 0.99982 | 0.99766 | 24.16 | 3.46 | 6.88 | 3.40 | 15.64 | 4.57 | 59 |
| Mato Grosso do Sul | ARIMA(0,2,1) | 0.99860 | 0.99966 | 0.99600 | 4.88 | 5.40 | 5.06 | 2.37 | 3.36 | 0.78 | 53 |
| Mato Grosso | ARIMA(0,2,1) | 0.99828 | 0.99841 | 0.98654 | 6.76 | 6.03 | 7.75 | 3.54 | 4.96 | 1.58 | 47 |
| Pará | ARIMA(0,2,1) | 0.99868 | 0.99941 | 0.99191 | 71.56 | 5.52 | 9.5 | 4.44 | 41.76 | 19.46 | 49 |
| Paraíba | ARIMA(3,2,0) | 0.99931 | 0.99586 | 0.97577 | 15.11 | 3.91 | 13.92 | 3.37 | 8.52 | 3.42 | 55 |
| Pernambuco | ARIMA(0,2,1) | 0.99949 | 0.99955 | 0.99360 | 89.79 | 3.28 | 7.58 | 3.08 | 48.25 | 19.18 | 55 |
| Piauí | ARIMA(1,2,0) | 0.99928 | 0.99813 | 0.98266 | 10.28 | 4.00 | 7.2 | 1.12 | 6.41 | 2.55 | 48 |
| Paraná | ARIMA(0,2,2) | 0.99942 | 0.99949 | 0.99392 | 18.18 | 3.47 | 4.96 | 2.90 | 12.96 | 2.67 | 55 |
| Rio de Janeiro | ARIMA(0,2,2) | 0.99960 | 0.99918 | 0.99258 | 105.29 | 2.96 | 8.78 | 2.44 | 67.51 | 27.06 | 62 |
| Rio Grande do Norte | ARIMA(0,2,1) | 0.99741 | 0.99727 | 0.97657 | 34.52 | 7.37 | 8.24 | 4.36 | 18.31 | 6.99 | 55 |
| Rondônia | ARIMA(0,2,0) | 0.99819 | 0.99485 | 0.96633 | 14.40 | 6.20 | 10.61 | −0.09 | 7.98 | 2.19 | 47 |
| Roraima | ARIMA(0,2,0) | 0.97919 | 0.99321 | 0.94769 | 43.73 | 21.08 | 12.08 | 1.56 | 19.02 | 6.33 | 46 |
| Rio Grande do Sul | ARIMA(2,2,2) | 0.99882 | 0.99940 | 0.99278 | 27.95 | 5.10 | 7.56 | 2.71 | 17.73 | 6.35 | 57 |
| Santa Catarina | ARIMA(0,2,1) | 0.99254 | 0.99955 | 0.99562 | 96.88 | 12.41 | 6.72 | 4.25 | 38.95 | 17.18 | 55 |
| Sergipe | ARIMA(3,2,0) | 0.99598 | 0.99631 | 0.97041 | 18.97 | 9.11 | 9.84 | 1.39 | 7.93 | 3.22 | 53 |
| São Paulo | ARIMA(0,2,2) | 0.99917 | 0.99914 | 0.98688 | 411.73 | 4.14 | 9.96 | 4.26 | 243.34 | 74.83 | 71 |
| Tocantins | ARIMA(0,2,2) | 0.99785 | 0.99308 | 0.95766 | 5.52 | 6.76 | 10.02 | 2.40 | 3.07 | 1.20 | 49 |
| Brazil | ARIMA(0,2,1) | 0.99978 | 0.99718 | 0.97963 | 688.24 | 2.20 | 15.65 | −0.06 | 401.29 | 142.02 | 71 |