Table 2.
Forecasting performance for each model in the validation set for the 15 countries.
| Country (total populationa) and methods | Mean errorb | Root mean square errorb | Mean absolute errorb | Mean percentage errorb | Mean absolute percentage errorb | |
| United States (N=329,466,283) | ||||||
|
|
ARIMAc | –183,472.5153 | 229,501.345 | 183,888.691 | –0.9538265 | 0.9562102 |
|
|
FNNd | –197,967.69975 | 251,014.19 | 201,574.807 | –1.027988 | 1.048648 |
|
|
MLPe | 34,016.71589 | 45,932.609 | 35,569.561 | 0.1774821 | 0.1862749 |
|
|
LSTMf | –17,670.38 | 41,667.98 g | 31,092.06 | –0.09409045 | 0.1664009 |
| Canada (N=37,855,702) | ||||||
|
|
ARIMA | –3786.81463 | 4953.7659 | 3786.8146 | –0.6828342 | 0.6828342 |
|
|
FNN | –1902.8218773 | 3146.8161 | 2133.5721 | –0.3503041 | 0.3898707 |
|
|
MLP | –6056.7104430 | 7294.1933 | 6056.7104 | –1.094643 | 1.094643 |
|
|
LSTM | 306.1702 | 2272.551 | 1501.248 | 0.04896196 | 0.2723075 |
| Mexico (N=127,792,286) | ||||||
|
|
ARIMA | –3776.6237 | 6281.987 | 4841.2544 | 0.3501243 | 1.2391347 |
|
|
FNN | –15,894.200241 | 19,622.066 | 16,156.1290 | –1.145524 | 1.165534 |
|
|
MLP | –3551.381635 | 6534.119 | 5455.281 | –0.2517612 | 0.3969063 |
|
|
LSTM | –1137.118 | 2883.836 | 2334.178 | –0.08386455 | 0.1716616 |
| Brazil (N=212,559,409) | ||||||
|
|
ARIMA | –52,913.8661 | 69,053.95 | 54,328.55 | –0.7032164 | 0.7228866 |
|
|
FNN | –168,251.54394 | 204,577.061 | 168,251.544 | –2.240681 | 2.240681 |
|
|
MLP | –28,723.33938 | 43,395.965 | 31,117.856 | –0.3797225 | 0.412664 |
|
|
LSTM | –2746.457 | 16,085.02 | 14,347.73 | –0.03768765 | 0.1931052 |
| Argentina (N=45,195,777) | ||||||
|
|
ARIMA | 10,240.495912 | 12,832.6035 | 10,240.4959 | 0.6433934 | 0.6433934 |
|
|
FNN | 22,285.962404 | 26,555.128 | 22,285.9624 | 1.402042 | 1.402042 |
|
|
MLP | 10,914.143275 | 13,689.5539 | 10,929.6874 | 0.6857769 | 0.6867919 |
|
|
LSTM | 1253.045 | 3920.961 | 3202.607 | 0.07803485 | 0.2024643 |
| Chile (N=19,116,209) | ||||||
|
|
ARIMA | 1823.55216 | 1992.35 | 1823.5522 | 0.3048502 | 0.3048502 |
|
|
FNN | 8171.7723060 | 9157.9881 | 8171.7723 | 1.363951 | 1.363951 |
|
|
MLP | 2169.702307 | 2435.4540 | 2169.7023 | 0.3622628 | 0.3622628 |
|
|
LSTM | 595.9308 | 790.8397 | 648.5224 | 0.1001373 | 0.1090634 |
| United Kingdom (N=67,886,004) | ||||||
|
|
ARIMA | 40,161.7481 | 55,436.735 | 41,580.2155 | 1.7053944 | 1.776331 |
|
|
FNN | –17,129.950943 | 23,936.144 | 17,129.951 | –0.7304511 | 0.7304511 |
|
|
MLP | 81,031.84 | 102,155.3238 | 81,031.841 | 3.482155 | 3.482155 |
|
|
LSTM | 15,560.98 | 17,735.29 | 15,560.98 | 0.6832804 | 0.6832804 |
| France (N=65,273,512) | ||||||
|
|
ARIMA | 1807.5070 | 8181.384 | 6633.665 | 0.07287266 | 0.2565254 |
|
|
FNN | 61,075.99023 | 67,684.575 | 61,075.990 | 2.340844 | 2.340844 |
|
|
MLP | 9601.594851 | 11,456.382 | 10,239.308 | 0.3726648 | 0.3969022 |
|
|
LSTM | 6262.693 | 9254.264 | 7784.804 | 0.241549 | 0.3000627 |
| Greece (N=10,423,056) | ||||||
|
|
ARIMA | 5423.2143 | 6072.0773 | 5423.2143 | 4.003338 | 4.003338 |
|
|
FNN | –21.8694361 | 561.98452 | 400.61927 | –0.01977488 | 0.2937978 |
|
|
MLP | –1145.165405 | 1341.1596 | 1145.1654 | –0.844399 | 0.844399 |
|
|
LSTM | –512.1191 | 565.7909 | 512.1191 | –0.3821559 | 0.3821559 |
| Taiwan (N=23,816,775) | ||||||
|
|
ARIMA | –15.97434477 | 17.288501 | 15.97434 | –2.0379969 | 2.037997 |
|
|
FNN | –6.571007146 | 7.379679 | 6.571007 | –0.84606232 | 0.8460623 |
|
|
MLP | –9.485179 | 12.925238 | 9.9162023 | –1.2005706 | 1.257011 |
|
|
LSTM | –2.059649 | 3.322996 | 2.978151 | –0.3227033 | 0.3820354 |
| Thailand (N=69,799,978) | ||||||
|
|
ARIMA | 1471.082153 | 1620.87009 | 1471.082153 | 23.7842238 | 23.784224 |
|
|
FNN | 1463.109910 | 1611.239573 | 1463.109910 | 23.659524 | 23.659524 |
|
|
MLP | 1517.21984066 | 1674.585004 | 1517.219841 | 24.5165025 | 24.516502 |
|
|
LSTM | 173.2286 | 308.695 | 202.2714 | 2.950519 | 3.435209 |
| South Korea (N=51,269,183) | ||||||
|
|
ARIMA | –260.265311 | 317.53169 | 265.29603 | –0.4540395 | 0.4641688 |
|
|
FNN | –75.7162332 | 181.29894 | 154.2065 | –0.1226205 | 0.2708482 |
|
|
MLP | –1138.0352476 | 1419.83911 | 1145.57606 | –1.963196 | 1.978379 |
|
|
LSTM | 323.9709 | 342.9156 | 323.9709 | 0.5978793 | 0.5978793 |
| India (N=1,380,004,385) | ||||||
|
|
ARIMA | 19,113.77834 | 21,947.375 | 19,113.778 | 0.1874688 | 0.1874688 |
|
|
FNN | –10,156.962689 | 13,612.018 | 10,156.963 | –0.09945817 | 0.09948717 |
|
|
MLP | 20,964.3576266 | 24,556.936 | 20,964.358 | 0.2055718 | 0.20055718 |
|
|
LSTM | –13,037.64 | 14,480.91 | 13,037.64 | –0.128178 | 0.1281378 |
| Australia (N=25,459,700) | ||||||
|
|
ARIMA | 26.9606020 | 30.40208 | 26.96060 | 0.09542063 | 0.09542063 |
|
|
FNN | 187.8959192 | 205.6998 | 187.89592 | 0.6634038 | 0.6637038 |
|
|
MLP | –15.69085695 | 76.48186 | 62.261210 | –0.05478576 | 0.2197826 |
|
|
LSTM | 5.898776 | 14.39023 | 11.91991 | 0.02086999 | 0.04212132 |
| Egypt (N=102,334,403) | ||||||
|
|
ARIMA | 2392.285714 | 3239.04732 | 2392.28571 | 1.7844594 | 1.784459 |
|
|
FNN | 1944.5586880 | 2641.98168 | 1944.55869 | 1.45017 | 1.45017 |
|
|
MLP | 669.96030638 | 936.05245 | 669.96031 | 0.4988667 | 0.4988667 |
|
|
LSTM | 437.0412 | 500.6487 | 438.0092 | 0.3304228 | 0.3311979 |
aTotal population in 2020.
bFive commonly used measures for evaluation of forecasting include mean error, root mean square error (RMSE), mean absolute error (MAE), mean percentage error, and mean absolute percentage error (MAPE), according to the records of the latest 14 days in 2020. The RMSE, MAE, and MAPE are always positive values.
cARIMA: autoregressive integrated moving average.
dFNN: feedforward neural network.
eMLP: multilayer perceptron.
fLSTM: long short-term memory.
gThe values for best performances in each country are italicized.