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Table 4 Comparison of the forecast performance of each model

From: A multivariate multi-step LSTM forecasting model for tuberculosis incidence with model explanation in Liaoning Province, China

Model

RMSE

MAE

MAPE (%)

sMAPE (%)

6-step ahead prediction between January 2016 to June 2016

 A

0.3244 (−)

0.2811 (−)

6.0454 (−)

5.8097 (−)

 B

1.0157 (+ 213.10%)

0.9339 (+ 232.23%)

20.0035 (+ 230.89%)

17.9006 (+ 208.12%)

 \(\varvec{C}^{\star }\)

0.2825 (− 12.92%)

0.2363 (− 15.94%)

5.0797 (− 15.97%)

4.9490 (− 14.81%)

 \(D^{\star }\)

0.4659 (+ 43.62%)

0.3206 (+ 14.05%)

6.8661 (+ 13.58%)

7.4156 (+ 27.64%)

12-step ahead prediction between January 2016 and December 2016

 A

0.4425 (−)

0.3917 (−)

9.7674 (−)

9.1462 (−)

 B

0.7825 (+ 63.40%)

0.6508 (+ 66.15%)

14.5400 (+ 48.86%)

13.2301 (+ 44.65%)

 \(C^{\star }\)

0.4060 (− 8.25%)

0.3073 (− 21.55%)

7.8076 (− 20.06%)

7.5203 (− 17.78%)

 \(\varvec{D}^{\star }\)

0.3753 (− 15.19%)

0.2619 (− 33.14%)

6.1742 (− 36.79%)

6.4240 (− 29.76%)

24-step ahead prediction between January 2016 and December 2017

 A

0.4672 (−)

0.4177 (−)

9.9328 (−)

9.3198 (−)

 B

0.7634 (+ 63.40%)

0.6384 (+ 52.84%)

14.1518 (+ 42.48%)

13.0495 (+ 40.02%)

 \(C^{\star }\)

0.4108 (− 12.07%)

0.3295 (− 21.12%)

7.7436 (− 22.04%)

7.4895 (− 19.64%)

 \(\varvec{D}^{\star }\)

0.4042 (− 13.48%)

0.3070 (− 26.50%)

6.9664 (− 29.86%)

7.2245 (− 22.48%)

  1. The data format x(y), x is the error value and y is the percentage change compared to the ARIMA model. Particularly, (–) indicates the null value. A is the ARIMA model and B is the SARIMA model. The new model proposed in this paper is labeled by superscript \(\star\). \(C^{\star }\) is the multivariate 2-step LSTM model and \(D^{\star }\) is the 3-step ARIMA–LSTM hybrid forecasting model