Web viewEstimating the Prevalence and Mortality of Coronavirus Disease 2019 (COVID-19) in the USA,...
Transcript of Web viewEstimating the Prevalence and Mortality of Coronavirus Disease 2019 (COVID-19) in the USA,...
Estimating the Prevalence and Mortality of Coronavirus Disease 2019 (COVID-19) in the USA, the UK, Russia, and India
Yongbin Wang1,*, Chunjie Xu2,*, Sanqiao Yao1, Yingzheng Zhao1, Yuchun Li1, Lei Wang3, Xiangmei Zhao1
1 Department of Epidemiology and Health Statistics, School of Public Health, Xinxiang Medical University, Xinxiang, Henan Province, P.R. China; 2 Department of Occupational and Environmental Health, School of Public Health, Capital Medical University, Beijing, P.R. China; 3 Center for Musculoskeletal Surgery, Charité – Universitätsmedizin Berlin, Corporate Member of Freie Universität Berlin, Humboldt-Universität zu Berlin and Berlin Institute of Health, Berlin, Germany
Correspondence: Yongbin Wang
Department of Epidemiology and Health Statistics, School of Public Health, Xinxiang Medical University, Xinxiang 453000, Henan Province, P.R. China
Tel +86 0373 383 1646
Email [email protected] (Yongbin Wang)
*These authors contributed equally to this work
Table S1 The degrees of difference for the prevalence and mortality time series in the USA, the UK, Russia, and India
Degree of difference
USA
UK
Russia
India
ADF
p-value
ADF
p-value
ADF
p-value
ADF
p-value
Prevalence data
Actual series
1.359
0.955
0.851
0.884
4.707
0.990
4.803
0.990
First-order difference
-0.517
0.448
-0.595
0.423
-3.692
<0.001
2.413
0.990
Second-order difference
-9.660
<0.001
-10.551
<0.001
-
-
-10.054
<0.001
Mortality data
Actual series
2.932
0.990
3.846
0.990
4.695
0.990
5.255
0.990
First-order difference
-1.337
0.187
-1.364
0.159
-0.035
0.601
-0.128
0.572
Second-order difference
-9.545
<0.001
-5.684
<0.001
-10.991
<0.001
-10.694
<0.001
Abbreviation: ADF Augmented Dickey–Fuller test.
Table S2 Comparisons of possible ARIMA models developed with the prevalence and mortality of COVID-19 in these four countries.
Country
Model
MAD
MAPE
RMSE
NBIC
Stationary R2
R2
USA
Possible ARIMA models developed with the square root transformed training prevalence data
ARIMA(0,2,1)
2575.215
25.784
3963.240
16.629
0.418
1.000
ARIMA(1,2,0)
2778.711
27.850
4202.739
16.746
0.365
1.000
ARIMA(2,2,0)
2853.595
26.567
4325.661
16.863
0.419
1.000
ARIMA(3,2,0)
2788.448
26.068
4409.395
16.961
0.447
1.000
ARIMA(1,2,1)
2760.484
25.648
4223.747
16.816
0.451
1.000
Possible ARIMA models developed with the square root transformed training mortality data
ARIMA(0,2,1)
210.036
10.237
336.582
11.706
0.237
1.000
ARIMA(1,2,0)
212.551
10.311
344.3451
11.752
0.161
1.000
ARIMA(1,2,1)
210.528
10.277
340.054
11.795
0.237
1.000
ARIMA(2,2,0)
211.971
10.276
344.453
11.820
0.226
1.000
ARIMA(0,2,2)
210.826
10.270
340.463
11.797
0.237
1.000
UK
Possible ARIMA models developed with the square root transformed training prevalence data
ARIMA(0,2,(1,6))
394.614
5.874
589.361
13.190
0.370
1.000
ARIMA(0,2,1)
475.356
6.483
795.262
13.417
0.194
1.000
ARIMA(0,2,2)
465.782
6.645
790.769
13.465
0.208
1.000
ARIMA(1,2,2)
455.907
6.581
776.964
13.489
0.241
1.000
ARIMA(2,2,2)
452.707
6.588
767.021
13.523
0.269
1.000
Possible ARIMA models developed with the log-transformed training mortality data
ARIMA(0,2,1)
451.222
11.931
714.520
13.215
0.391
0.994
ARIMA(1,2,0)
361.356
11.984
775.004
13.378
0.217
0.993
ARIMA(1,2,1)*
429.388
12.009
708.945
13.271
0.397
0.994
ARIMA(2,2,0)#
358.292
10.952
746.063
13.373
0.329
0.993
ARIMA(0,2,2)#
387.669
11.899
675.339
13.174
0.407
0.994
Russia
Possible ARIMA models developed with the log-transformed training prevalence data
ARIMA(1,1,1)
832.455
9.166
1898.550
15.215
0.039
0.997
ARIMA(0,1,1)
1081.249
10.369
2158.841
15.413
-0.316
0.996
ARIMA(1,1,0)
879.934
9.827
1909.207
15.168
-0.243
0.997
ARIMA(2,1,1)
1243.922
13.078
2803.403
16.053
-0.225
0.994
Possible ARIMA models developed with the log-transformed training mortality data
ARIMA(0,2,1)
19.138
10.721
30.685
6.969
0.410
0.994
ARIMA(0,2,0)
20.385
12.242
32.884
7.084
0.000
0.993
ARIMA(1,2,0)
20.319
11.752
31.538
7.000
0.184
0.994
ARIMA(2,2,0)
19.621
10.362
31.847
7.117
0.466
0.994
ARIMA(0,2,2)
18.350
10.527
32.233
7.141
0.443
0.994
India
Possible ARIMA models developed with the square root transformed training prevalence data
ARIMA(2,2,1)
113.639
28.303
202.730
10.861
0.611
1.000
ARIMA(1,2,1)
119.206
29.502
205.414
10.828
0.582
1.000
ARIMA(1,2,0)
144.142
33.264
246.230
11.156
0.338
1.000
ARIMA(0,2,1)
173.786
44.036
293.548
11.423
0.000
0.999
ARIMA(1,2,2)
117.076
28.868
205.335
10.887
0.598
1.000
ARIMA(2,2,0)
116.233
27.793
212.830
10.899
0.544
1.000
Possible ARIMA models developed with the training mortality data
ARIMA(0,2,2)
6.387
30.482
8.381
4.487
0.522
1.000
ARIMA(0,2,1)
6.897
32.795
8.990
4.549
0.438
0.999
ARIMA(1,2,0)
6.771
15.787
9.453
4.571
0.366
0.999
ARIMA(1,2,1)
6.484
32.222
8.560
4.529
0.501
1.000
ARIMA(2,2,0)
6.440
30.588
8.425
4.497
0.517
1.000
Abbreviation: ARIMA Autoregressive integrated moving average method, MAD Mean absolute deviation, MAPE Mean absolute percentage error, RMSE Root mean squared error, NBIC Normalized Bayesian information criterion.
* indicates no statistical difference of the estimated parameters.
# indicates a p-value less than 0.05 under the Ljung-Box Q test.
Table S3 The candidate ETS models and their goodness of test results for the COVID-19 prevalence series in the USA
Model
Compact LL
Likelihood
AIC
BIC
HQ
AMSE
M,MD,N
-760.290
-706.041
1530.580
1542.100
1535.180
9.90E+07
M,M,N
-761.392
-707.143
1530.780
1540.000
1534.460
2.60E+08
M,MD,M
-759.462
-705.213
1530.920
1544.750
1536.440
9.60E+07
M,M,M
-760.573
-706.324
1531.150
1542.670
1535.740
2.50E+08
M,MD,A
-760.290
-706.041
1532.580
1546.400
1538.100
9.90E+07
M,M,A
-761.392
-707.143
1532.780
1544.310
1537.380
2.60E+08
M,A,M
-764.985
-710.736
1539.970
1551.490
1544.570
7.10E+07
M,A,N
-766.251
-712.002
1540.500
1549.720
1544.180
8.30E+07
M,AD,M
-764.985
-710.736
1541.970
1555.800
1547.490
7.10E+07
A,A,N
-766.986
-712.737
1541.970
1551.190
1545.650
6.40E+07
M,AD,N
-766.251
-712.002
1542.500
1554.020
1547.100
1.00E+100
M,A,A
-766.251
-712.002
1542.500
1554.020
1547.100
8.30E+07
A,A,A
-766.628
-712.379
1543.260
1554.780
1547.850
6.30E+07
A,A,M
-766.740
-712.491
1543.480
1555.000
1548.080
6.30E+07
A,AD,N
-766.986
-712.737
1543.970
1555.490
1548.570
6.40E+07
M,AD,A
-766.251
-712.002
1544.500
1558.330
1550.020
1.00E+100
A,AD,A
-766.628
-712.379
1545.260
1559.080
1550.770
6.30E+07
A,MD,A
-766.701
-712.452
1545.400
1559.230
1550.920
6.80E+07
A,AD,M
-766.740
-712.491
1545.480
1559.310
1551.000
1.00E+100
A,MD,M
-766.913
-712.665
1545.830
1559.650
1551.340
5.80E+07
A,MD,N
-769.312
-715.063
1548.620
1560.140
1553.220
6.40E+07
A,M,A
-781.991
-727.742
1573.980
1585.500
1578.580
1.80E+08
A,M,N
-784.092
-729.843
1576.180
1585.400
1579.860
2.10E+08
A,M,M
-783.675
-729.426
1577.350
1588.870
1581.950
1.90E+08
M,N,N
-790.107
-735.858
1584.210
1588.820
1586.050
1.80E+09
M,N,M
-789.259
-735.010
1584.520
1591.430
1587.270
1.80E+09
M,N,A
-789.424
-735.175
1584.850
1591.760
1587.610
1.60E+09
A,N,A
-849.408
-795.159
1704.820
1711.730
1707.570
1.20E+09
A,N,M
-859.652
-805.403
1725.300
1732.220
1728.060
1.30E+09
A,N,N
-892.635
-838.386
1789.270
1793.880
1791.110
1.80E+09
Abbreviation: ETS Error-trend-seasonal method, LL Log-likelihood, AIC Akaike information criterion, BIC Bayesian information criterion, HQ Hannan-Quinn criterion, AMSE Average mean square error.
Table S4 The candidate ETS models and their goodness of test results for the COVID-19 prevalence series in the UK
Model
Compact LL
Likelihood
AIC
BIC
HQ
AMSE
A,AD,M
-650.859
-596.610
1313.720
1327.540
1319.230
2219036.000
A,AD,N
-651.998
-597.749
1314.000
1325.520
1318.590
2193585.000
A,AD,A
-651.119
-596.870
1314.240
1328.060
1319.750
2275837.000
Abbreviation: ETS Error-trend-seasonal method, LL Log-likelihood, AIC Akaike information criterion, BIC Bayesian information criterion, HQ Hannan-Quinn criterion, AMSE Average mean square error.
Table S5 The candidate ETS models and their goodness of test results for the COVID-19 prevalence series in Russia
Model
Compact LL
Likelihood
AIC
BIC
HQ
AMSE
A,MD,A
-687.149
-632.900
1386.300
1400.120
1391.810
1936007
A,MD,N
-692.184
-637.935
1394.370
1405.890
1398.960
2557242
A,MD,M
-694.749
-640.500
1401.500
1415.320
1407.010
2952685
A,M,N
-706.350
-652.101
1420.700
1429.920
1424.380
5433736
A,A,N
-706.562
-652.313
1421.120
1430.340
1424.800
5634054
A,M,A
-705.645
-651.396
1421.290
1432.810
1425.890
5296611
A,A,M
-705.951
-651.702
1421.900
1433.420
1426.500
5615841
A,M,M
-706.237
-651.988
1422.470
1433.990
1427.070
5464416
A,A,A
-706.562
-652.313
1423.120
1434.640
1427.720
5634061
A,AD,N
-706.562
-652.313
1423.120
1434.640
1427.720
1.00E+100
A,AD,M
-705.951
-651.702
1423.900
1437.730
1429.420
5615835
A,AD,A
-706.562
-652.313
1425.120
1438.950
1430.640
1.00E+100
A,N,A
-742.488
-688.239
1490.980
1497.890
1493.730
3.50E+07
A,N,M
-743.223
-688.974
1492.450
1499.360
1495.200
3.50E+07
A,N,N
-763.140
-708.892
1530.280
1534.890
1532.120
4.60E+07
Abbreviation: ETS Error-trend-seasonal method, LL Log-likelihood, AIC Akaike information criterion, BIC Bayesian information criterion, HQ Hannan-Quinn criterion, AMSE Average mean square error.
Table S6 The candidate ETS models and their goodness of test results for the COVID-19 prevalence series in India
Model
Compact LL
Likelihood
AIC
BIC
HQ
AMSE
A,M,A
-560.728
-506.479
1131.460
1142.980
1136.050
180865
A,M,N
-562.179
-507.930
1132.360
1141.570
1136.030
188234
A,M,M
-562.001
-507.752
1134.000
1145.520
1138.600
186684
Abbreviation: ETS Error-trend-seasonal method, LL Log-likelihood, AIC Akaike information criterion, BIC Bayesian information criterion, HQ Hannan-Quinn criterion, AMSE Average mean square error.
Table S7 The candidate ETS models and their goodness of test results for the COVID-19 mortality series in the USA
Model
Compact LL
Likelihood
AIC
BIC
HQ
AMSE
M,A,M
-473.070
-433.103
956.139
966.775
960.315
499399
M,A,N
-474.723
-434.756
957.447
965.955
960.787
517943
M,AD,M
-473.07
-433.103
958.139
970.902
963.150
499399
M,A,A
-474.723
-434.756
959.447
970.082
963.622
517943
M,AD,N
-474.723
-434.756
959.447
970.082
963.622
517943
M,AD,A
-474.723
-434.756
961.447
974.209
966.458
517943
A,A,N
-487.289
-447.322
982.579
991.087
985.919
468447
A,A,M
-486.996
-447.029
983.993
994.628
988.168
443598
A,A,A
-487.129
-447.162
984.258
994.894
988.434
453610
A,AD,N
-487.289
-447.322
984.579
995.214
988.754
468447
A,AD,M
-486.996
-447.029
985.993
998.755
991.004
443598
A,AD,A
-487.129
-447.162
986.258
999.021
991.269
453610
A,M,N
-491.889
-451.922
991.779
1000.290
995.119
752382
A,M,M
-493.755
-453.788
997.509
1008.140
1001.680
2428769
M,M,A
-499.414
-459.447
1008.830
1019.460
1013.000
2805910
M,N,A
-502.593
-462.626
1011.190
1017.570
1013.690
6951721
M,N,N
-520.290
-480.323
1044.580
1048.830
1046.250
7934603
M,N,M
-520.290
-480.323
1046.580
1052.960
1049.090
7934603
M,M,N
-537.515
-497.548
1083.030
1091.540
1086.370
1.80E+15
A,N,A
-539.835
-499.868
1085.670
1092.050
1088.180
5125265
A,N,M
-545.419
-505.452
1096.840
1103.220
1099.340
5411203
M,M,M
-545.998
-506.031
1102.000
1112.630
1106.170
1.50E+10
A,N,N
-575.295
-535.328
1154.590
1158.840
1156.260
7934597
A,M,A
-583.379
-543.413
1176.760
1187.390
1180.930
1.00E+07
M,MD,M
1.00E+100
1.00E+100
1.00E+100
1.00E+100
1.00E+100
1.50E+10
M,MD,A
1.00E+100
1.00E+100
1.00E+100
1.00E+100
1.00E+100
3.30E+12
A,MD,M
1.00E+100
1.00E+100
1.00E+100
1.00E+100
1.00E+100
2428769
A,MD,N
1.00E+100
1.00E+100
1.00E+100
1.00E+100
1.00E+100
6.90E+08
M,MD,N
1.00E+100
1.00E+100
1.00E+100
1.00E+100
1.00E+100
3.30E+12
A,MD,A
1.00E+100
1.00E+100
1.00E+100
1.00E+100
1.00E+100
6.90E+08
Abbreviation: ETS Error-trend-seasonal method, LL Log-likelihood, AIC Akaike information criterion, BIC Bayesian information criterion, HQ Hannan-Quinn criterion, AMSE Average mean square error.
Table S8 The candidate ETS models and their goodness of test results for the COVID-19 mortality series in the UK
Model
Compact LL
Likelihood
AIC
BIC
HQ
AMSE
M,A,N
-443.898
-408.444
895.796
904.038
899.006
855802
M,M,A
-442.983
-407.529
895.966
906.268
899.979
1172589
M,A,A
-443.898
-408.444
897.796
908.098
901.809
855802
M,A,M
-443.898
-408.444
897.796
908.098
901.809
855802
M,AD,N
-443.898
-408.444
897.796
908.098
901.809
1.E+100
M,AD,A
-443.898
-408.444
899.796
912.159
904.612
1.E+100
M,AD,M
-443.898
-408.444
899.796
912.159
904.612
1.E+100
M,MD,N
-449.948
-414.493
909.895
920.198
913.908
748767
M,M,N
-462.610
-427.155
933.220
941.461
936.430
1.0E+07
M,M,M
-462.610
-427.155
935.220
945.522
939.233
1.0E+07
M,N,A
-469.275
-433.820
944.549
950.731
946.957
2242613
M,MD,M
-469.275
-433.820
950.549
962.912
955.365
2242613
M,MD,A
-475.221
-439.767
962.443
974.805
967.258
835092
M,N,N
-481.194
-445.740
966.389
970.510
967.994
2328564
A,MD,N
-479.009
-443.555
968.018
978.320
972.031
500493
A,MD,A
-478.800
-443.346
969.601
981.964
974.416
489780
A,MD,M
-478.948
-443.494
969.896
982.259
974.712
496689
A,A,N
-482.619
-447.165
973.239
981.481
976.449
647994.
A,A,M
-481.678
-446.224
973.356
983.658
977.369
608757
A,A,A
-482.619
-447.165
975.239
985.541
979.252
647994
A,AD,N
-482.619
-447.165
975.239
985.541
979.252
647994
A,AD,M
-481.680
-446.225
975.359
987.722
980.175
609549
A,AD,A
-482.619
-447.165
977.239
989.602
982.054
647995
A,M,N
-488.521
-453.067
985.042
993.284
988.252
993397
A,M,M
-488.518
-453.063
987.035
997.338
991.048
1112650
A,M,A
-490.240
-454.786
990.480
1000.78
994.493
1028873
A,N,A
-497.731
-462.277
1001.46
1007.64
1003.87
1855772
A,N,M
-498.380
-462.926
1002.76
1008.94
1005.17
1874168
A,N,N
-504.743
-469.288
1013.49
1017.61
1015.09
2188041
M,N,M
-544.682
-509.228
1095.36
1101.55
1097.77
1964958
Abbreviation: ETS Error-trend-seasonal method, LL Log-likelihood, AIC Akaike information criterion, BIC Bayesian information criterion, HQ Hannan-Quinn criterion, AMSE Average mean square error.
Table S9 The candidate ETS models and their goodness of test results for the COVID-19 mortality series in Russia
Model
Compact LL
Likelihood
AIC
BIC
HQ
AMSE
A,A,N
-192.823
-176.722
393.646
400.301
396.034
1445.800
A,A,M
-192.389
-176.288
394.778
403.096
397.763
1404.480
A,A,A
-192.823
-176.722
395.646
403.964
398.631
1445.800
A,MD,N
-192.831
-176.730
395.662
403.980
398.646
1157.690
A,AD,N
-192.839
-176.739
395.679
403.997
398.663
1452.790
A,AD,M
-192.389
-176.288
396.778
406.760
400.360
1404.460
A,AD,A
-192.823
-176.722
397.646
407.628
401.228
1445.800
A,MD,M
-192.831
-176.730
397.662
407.643
401.243
1157.690
A,MD,A
-192.831
-176.730
397.662
407.643
401.243
1157.690
A,M,A
-196.511
-180.410
403.022
411.339
406.006
1993.970
A,M,N
-197.675
-181.574
403.350
410.004
405.738
1.2E+07
M,A,N
-200.675
-184.574
409.349
416.004
411.737
2927.060
M,A,A
-200.675
-184.574
411.349
419.667
414.334
2927.020
M,AD,N
-200.675
-184.574
411.349
419.667
414.334
1.E+100
M,A,M
-200.675
-184.574
411.349
419.667
414.334
2927.360
M,AD,A
-200.675
-184.574
413.349
423.331
416.931
1.E+100
M,AD,M
-200.675
-184.574
413.350
423.331
416.931
1.E+100
M,MD,N
-206.338
-190.238
422.677
430.995
425.661
7672.630
M,MD,M
-206.338
-190.238
424.677
434.658
428.258
7672.630
M,MD,A
-206.338
-190.238
424.677
434.658
428.258
7672.630
A,N,A
-210.007
-193.906
426.015
431.005
427.805
6718.520
A,N,M
-210.288
-194.187
426.575
431.566
428.366
6753.640
M,M,A
-215.253
-199.152
440.506
448.823
443.490
1763.000
A,N,N
-221.743
-205.642
447.486
450.813
448.680
9088.170
M,N,N
-222.030
-205.929
448.060
451.387
449.253
13619.700
M,N,M
-222.030
-205.929
450.060
455.050
451.850
13619.700
M,N,A
-222.030
-205.929
450.060
455.050
451.850
13619.700
M,M,N
-274.553
-258.452
557.106
563.761
559.494
29257.200
A,M,M
-340.970
-324.869
691.940
700.258
694.925
2928109
M,M,M
-370.251
-354.150
750.502
758.820
753.486
2934296
Abbreviation: ETS Error-trend-seasonal method, LL Log-likelihood, AIC Akaike information criterion, BIC Bayesian information criterion, HQ Hannan-Quinn criterion, AMSE Average mean square error.
Table S10 The candidate ETS models and their goodness of test results for the COVID-19 mortality series in India
Model
Compact LL
Likelihood
AIC
BIC
HQ
AMSE
M,M,N
-239.521
-210.573
487.041
494.846
490.034
1766.340
M,M,M
-239.444
-210.496
488.887
498.644
492.628
1623.790
M,M,A
-239.490
-210.542
488.980
498.736
492.720
1803.180
Abbreviation: ETS Error-trend-seasonal method, LL Log-likelihood, AIC Akaike information criterion, BIC Bayesian information criterion, HQ Hannan-Quinn criterion, AMSE Average mean square error.
Table S11 Estimated initial parameters of the best-fitting ETS methods for the prevalence and mortality of COVID-19 in the USA, the UK, Russia, and India
Country
Initial parameters
Value
USA
Prevalence data of COVID-19
Initial level
9.846
Initial trend
1.615
Mortality data of COVID-19
Initial level
-1.518
Initial trend
3.494
Initial state 1
1.000
UK
Prevalence data of COVID-19
Initial level
8.303
Initial trend
0.902
Initial state 1
1.000
Mortality data of COVID-19
Initial level
-11.055
Initial trend
-7.981
Russia
Prevalence data of COVID-19
Initial level
-0.174
Initial trend
0.276
Initial state 1
0.000
Mortality data of COVID-19
Initial level
-0.169
Initial trend
2.118
India
Prevalence data of COVID-19
Initial level
1.553
Initial trend
-0.137
Initial state 1
0.000
Mortality data of COVID-19
Initial level
1.502
Initial trend
1.138
Table S12 Estimated parameters of the best-fitting ETS methods developed with the whole data and their goodness of fit test results for the prevalence and mortality of COVID-19 in these four countries
Country
Parameter
Compact LL
LL
AIC
BIC
HQ
AMSE
USA
ETS(A,AD,N) model developed with the whole prevalence data
α=0.935
-924.898
-855.390
1864.447
1879.173
1864.730
8.3E+07
β=0.470
γ=0.000
δ=0.980
ETS(A,AD,N) model developed with the whole mortality data
α=1.000
-636.933
-582.684
1493.271
1507.997
1288.462
1359916
β=0.356
γ=0.000
δ=0.980
UK
ETS(A,AD,N) model developed with the whole prevalence data
α=1.000
-764.541
-695.032
1543.094
1557.820
1544.020
1.0E+100
β=0.562
γ=0.000
δ=0.980
ETS(A,AD,N) model developed with the whole mortality data
α=1.000
-585.244
-535.872
1450.410
1465.136
1184.953
653458
β=0.183
γ=0.000
δ=0.980
Russia
ETS(M,MD,N) model developed with the whole prevalence data
α=0.153
-656.837
-587.329
1329.626
1344.352
1328.612
1.4E+07
β=0.153
γ=0.000
δ=0.980
ETS(A,AD,N) model developed with the whole mortality data
α=0.949
-254.106
-226.210
874.080
888.806
521.903
1266.265
β=0.439
γ=0.000
δ=0.980
India
ETS(A,AD,N) model developed with the whole prevalence data
α=0.666
-673.707
-604.199
1369.245
1383.971
1362.353
1.0E+100
β=0.666
γ=0.000
δ=0.980
ETS(A,AD,N) model developed with the whole mortality data
α=0.955
-360.843
-318.571
882.907
897.633
735.938
3109.498
β=0.451
γ=0.000
δ=0.980
Abbreviation: ETS Error-trend-seasonal method, LL Log-likelihood, AIC Akaike information criterion, BIC Bayesian information criterion, HQ Hannan-Quinn criterion, AMSE Average mean square error.
Figure S1 Modeling process for time series forecasting with an ARIMA model.
Figure S2 Autocorrelation function (ACF) and partial ACF (PACF) of the differenced COVID-19 prevalence series for (A) USA, (B) UK, (C) Russia, and (D) India. Generally, the ACF offers a considerable amount of information on the order of moving average parameters, while the PACF offers a considerable amount of information on the order of autoregressive parameters. A search for the optimum p and q can be done by comparing the R2, stationary R2, and normalized Bayesian information criterion (NBIC) repeatedly.
Figure S3 Autocorrelation function (ACF) and partial ACF (PACF) of the differenced COVID-19 mortality series for (A) USA, (B) UK, (C) Russia, and (D) India. Typically, the ACF offers a considerable amount of information on the order of moving average parameters, while the PACF offers a considerable amount of information on the order of autoregressive parameters. A search for the optimum p and q can be done by comparing the R2, stationary R2, and normalized Bayesian information criterion (NBIC) repeatedly.