You are viewing the site in preview mode
Skip to main content

realtime

forecast 1 week

forecast 2 week

forecast 3 week


RMSE

ARGO

0.315

0.435

0.487

0.459

Ref. [11]

0.469

0.544

0.590

0.578

ar4

0.944

0.954

0.935

0.902

naive

1 (0.374)

1 (0.613)

1 (0.756)

1 (0.869)

MAE

ARGO

0.403

0.446

0.456

0.426

Ref. [11]

0.497

0.614

0.603

0.593

ar4

0.895

0.880

0.872

0.867

naive

1 (0.221)

1 (0.363)

1 (0.480)

1 (0.575)

RMSPE

ARGO

0.449

0.474

0.504

0.461

Ref. [11]

0.655

0.677

0.657

0.691

ar4

1.001

1.018

1.032

1.044

naive

1 (0.126)

1 (0.194)

1 (0.246)

1 (0.293)

MAPE

ARGO

0.481

0.458

0.454

0.419

Ref. [11]

0.625

0.704

0.662

0.676

ar4

0.956

0.965

0.977

0.988

naive

1 (0.101)

1 (0.156)

1 (0.205)

1 (0.251)

Correlation
    
ARGO

0.995

0.976

0.952

0.942

Ref. [11]

0.989

0.960

0.928

0.904

ar4

0.954

0.871

0.804

0.748

naive

0.951

0.867

0.796

0.727

Error reduction of ARGO over the best available alternative (in %)

RMSE

32.90
[16.38,55.54]

20.07
[5.13,31.38]

17.40
[1.29,28.82]

20.53
[11.82,27.33]

MAE

18.79
[0.23,36.67]

27.44
[10.28,39.18]

24.41
[7.66,34.53]

28.13
[15.84,36.38]

RMSPE

31.50
[21.63,40.84]

29.90
[9.42,41.95]

23.26
[4.69,33.00]

33.32
[19.94,41.69]

MAPE

22.92
[7.93,35.94]

34.95
[18.59,46.76]

31.42
[12.90,43.04]

38.02
[26.00,47.26]

 The evaluation metrics between the prediction \( \widehat{p_t} \) and the target \( \widehat{p_t} \) include RMSE \( \left(=\sqrt{\frac{1}{T}\sum_{t=1}^T{\left(\widehat{p_t}{p}_t\right)}^2}\right),\mathrm{MAE}\left(=\frac{1}{T}\sum_{t=1}^T\widehat{p_t}{p}_t\right),\mathrm{RMSPE}\left(=\sqrt{\frac{1}{T}\sum_{t=1}^T{\left(\frac{\widehat{p_t}{p}_t}{p_t}\right)}^2}\right),\mathrm{MAPE}\left(=\frac{1}{T}\sum_{t=1}^T\frac{\mid \widehat{p_t}{p}_t\mid }{p_t}\right) \), and Pearson correlation. The benchmark models include the ensemble method by Santillana et al. [11], an autoregression model with 4 lags, and a naive model, which uses prior week’s ILI level as the prediction for the current week as well as the next 3 weeks. Boldface highlights the best method for each metric in each forecasting time horizon. RMSE, MAE, RMSPE, MAPE are relative to the error of the naive method, i.e., the numbers are the ratio of the error of a given method over that of the naive method; the absolute error of the naive method is given in the round bracket. Table S3 in the Additional file 1 gives the absolute error of all methods. For each forecasting time horizon and each evaluation metrics, the error reduction of ARGO over the best alternative method is given in the second half of the table, together with 95% confidence intervals (in the square bracket) constructed using stationary bootstrap [33] with mean block size of 52 weeks.