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. 2024 Sep 28;68(12):2731–2742. doi: 10.1007/s00484-024-02785-4

Table 6.

Retrospective model statistics (1984–2023)

Ljung-Box Q(18)
# Location DV Model type St. R 2 R 2 RMSE MAPE Statistic df p Outliers
1 Atlantacc WBGT Simple Seasonal 0.72 0.95 1.70 214.65 15.78 16 0.468 0
Level 0 Winters' Additive 0.74 0.96 2.56 21.52 23.03 15 0.084 0
Level 1 Simple Seasonal 0.74 0.71 3.13 59.17 16.84 16 0.396 0
Level 2 Simple Seasonal 0.76 0.86 3.31 44.21 20.99 16 0.179 0
Level 3 Simple Seasonal 0.65 0.46 2.64 89.96 46.84 16 0.000 0
Level 4 Simple Seasonal 0.78 0.05 0.25 87.73 8.54 16 0.931 0
2 Boston WBGT Simple Seasonal 0.71 0.97 1.56 66.39 17.40 16 0.360 0
Level 0 Winters' Additive 0.65 0.94 2.33 20.99 32.03 15 0.006 0
Level 1 Simple Seasonal 0.68 0.88 2.27 35.72 24.94 16 0.071 0
Level 2 Simple Seasonal 0.69 0.67 2.13 64.97 8.24 16 0.941 0
Level 3 Winters’ Additive 0.77 0.20 0.45 65.18 13.51 15 0.563 0
3 Dallascc WBGT Simple Seasonal 0.71 0.96 1.53 24.49 18.01 16 0.323 0
Level 0 Winters’ Additive 0.76 0.97 2.37 20.01 15.57 15 0.411 0
Level 1 Simple Seasonal 0.71 0.67 2.68 58.21 17.79 16 0.336 0
Level 2 Winters’ Additive 0.71 0.71 3.30 63.79 21.05 15 0.135 0
Level 3 Simple Seasonal 0.73 0.76 3.40 78.80 8.28 16 0.940 0
Level 4 ARIMA(0,0,1)(0,1,1) 0.47 0.52 3.24 93.97 6.67 16 0.979 0
4 Houstoncc WBGT Simple Seasonal 0.71 0.95 1.44 7.42 15.28 16 0.504 0
Level 0 Simple Seasonal 0.72 0.92 3.10 28.20 17.62 16 0.347 0
Level 1 Simple Seasonal 0.71 0.61 3.13 67.61 20.59 16 0.195 0
Level 2 Simple Seasonal 0.72 0.73 3.36 64.91 21.66 16 0.154 0
Level 3 Simple Seasonal 0.66 0.84 3.86 50.95 23.28 16 0.106 0
Level 4 ARIMA(0,0,1)(1,1,1) 0.42 0.51 2.95 85.73 24.75 15 0.053 0
5 Kansas City WBGT Simple Seasonal 0.72 0.96 1.92 64.88 21.98 16 0.144 0
Level 0 Simple Seasonal 0.74 0.95 2.69 22.48 19.72 16 0.233 0
Level 1 Simple Seasonal 0.76 0.71 2.72 56.67 27.82 16 0.033 0
Level 2 Simple Seasonal 0.71 0.81 2.65 55.44 16.65 16 0.409 0
Level 3 Simple Seasonal 0.66 0.63 1.84 74.10 24.74 16 0.075 0
Level 4 ARIMA(0,0,1)(1,0,1) 0.27 0.27 0.86 79.33 15.03 15 0.449 0
6 Los Angelescc WBGT Simple Seasonal 0.67 0.93 1.16 7.91 30.10 16 0.018 0
Level 0 Simple Seasonal 0.67 0.83 3.75 22.96 39.74 16 0.000 0
Level 1 Simple Seasonal 0.69 0.81 3.46 56.80 29.99 16 0.018 0
Level 2 Simple Seasonal 0.73 0.33 1.75 74.27 13.93 16 0.604 0
Level 3 Simple Seasonal 0.75 0.03 0.16 95.13 28.76 16 0.026 0
7 Miami WBGT Simple Seasonal 0.67 0.91 0.90 2.86 41.27 16 0.000 0
Level 0 Winters’ Additive 0.72 0.56 2.47 78.91 26.30 15 0.035 0
Level 1 Simple Seasonal 0.73 0.75 3.48 57.10 32.72 16 0.008 0
Level 2 Simple Seasonal 0.69 0.68 4.98 62.75 16.85 16 0.396 0
Level 3 ARIMA (0,0,1)(0,1,1) 0.39 0.84 4.56 45.93 8.75 16 0.923 0
Level 4 ARIMA (1,0,0)(0,1,1) 0.50 0.72 3.12 104.87 27.38 16 0.037 0
8 New York WBGT Simple Seasonal 0.72 0.97 1.71 68.15 14.46 16 0.565 0
Level 0 Winters’ Additive 0.71 0.94 2.41 19.70 15.87 15 0.391 0
Level 1 Winters’ Additive 0.72 0.86 2.43 42.38 9.15 15 0.870 0
Level 2 Simple Seasonal 0.65 0.73 2.26 64.11 9.22 16 0.904 0
Level 3 Simple Seasonal 0.72 0.27 0.53 52.85 7.61 16 0.960 0
9 Philadelphia WBGT Simple Seasonal 0.72 0.97 1.70 151.63 11.79 16 0.758 0
Level 0 Winters’ Additive 0.74 0.96 2.30 15.57 29.87 15 0.012 0
Level 1 Simple Seasonal 0.73 0.79 2.69 50.10 11.64 16 0.768 0
Level 2 Simple Seasonal 0.75 0.85 2.14 49.19 17.85 16 0.333 0
Level 3 (0,0,1)(0,1,1) 0.50 0.50 1.09 65.57 11.88 16 0.752 0
Level 4 (0,0,0)(1,0,0) 0.13 0.13 0.19 85.54 0.73 17 1 0
10 San Francisco WBGT Simple Seasonal 0.67 0.92 1.09 9.06 26.70 16 0.045 0
Level 0 Simple Seasonal 0.68 0.47 1.99 4.81 22.45 16 0.129 0
Level 1 Simple Seasonal 0.69 0.48 1.89 76.67 22.74 16 0.121 0
Level 2 Simple Seasonal 0.75 0.05 0.32 90.04 21.55 16 0.158 0
Level 3 Simple Seasonal 0.76 0.02 0.09 97.65 0.34 16 1 0
11 Seattle WBGT Simple Seasonal 0.70 0.94 1.24 37.39 20.60 16 0.194 0
Level 0 Simple Seasonal 0.73 0.64 1.88 3.92 22.41 16 0.131 0
Level 1 Simple Seasonal 0.75 0.66 1.79 67.96 21.63 16 0.156 0
Level 2 Simple Seasonal 0.81 0.13 0.40 74.00 30.44 16 0.016 0
Level 3 Simple Seasonal 0.76 0.02 0.05 97.67 0.36 16 1 0
12 Guadalajara WBGT Simple Seasonal 0.67 0.92 0.82 4.25 36.92 16 0.002 0
Level 0 Simple Seasonal 0.59 0.92 3.38 36.25 25.04 16 0.069 0
Level 1 Simple Seasonal 0.58 0.92 3.38 32.48 27.11 16 0.040 0
Level 2 ARIMA(0,0,11)(1,1,1) 0.50 0.29 0.50 73.95 4.71 15 0.994 0
13 Guadalupe WBGT Simple Seasonal 0.68 0.95 1.14 5.90 18.41 16 0.300 0
Level 0 Simple Seasonal 0.67 0.95 2.93 27.55 39.44 16 0.000 0
Level 1 Simple Seasonal 0.67 0.67 3.88 69.16 27.42 16 0.037 0
Level 2 Winters’ Additive 0.69 0.92 3.22 39.74 22.11 15 0.105 0
Level 3 ARIMA(0,0,2)(1,0,1) 0.25 0.25 1.65 72.12 7.30 14 0.922 0
Level 4 Simple Seasonal 0.51 0.02 0.05 97.67 0.00 16 1 0
14 Mexico City WBGT Simple Seasonal 0.68 0.89 0.79 6.47 44.00 16 0.000 0
Level 0 Winters’ Multiplicative 0.81 0.98 0.13 0.13 42.66 15 0.000 0
15 Toronto WBGT Simple Seasonal 0.63 0.97 1.60 53.76 62.75 16 0.000 0
Level 0 ARIMA(1,0,0)(0,1,1) 0.40 0.84 3.15 19.33 19.93 16 0.223 0
Level 1 ARIMA(1,0,0)(0,1,1) 0.37 0.78 2.91 58.92 19.00 16 0.269 0
Level 2 ARIMA(1,0,0)(0,1,1) 0.40 0.45 1.99 70.05 14.49 16 0.562 0
Level 3 Simple Seasonal 0.70 0.05 0.22 89.51 12.76 16 0.690 0
16 Toronto WBGT Simple Seasonal 0.68 0.95 1.52 842.07 33.31 16 0.007 0
Level 0 Simple Seasonal 0.72 0.46 1.39 2.29 17.44 16 0.357 0
Level 1 Simple Seasonal 0.71 0.45 1.32 57.60 14.37 16 0.571 0
Level 2 Simple Seasonal 0.79 0.05 0.23 94.04 26.73 16 0.045 0
Level 3 Simple Seasonal 0.76 0.02 0.05 97.67 0.36 16 1 0