## 4 Empirical Results
### Past-Present-Future Framework  
In this study, the period from 2015 to 2019 was used as the past-present data to predict the 2020 future data. The forecast DEA and confidence intervals from 2021 to 2024 are shown in Appendix A Table A1. The prediction results of each DMU and the predicted score, confidence interval, and efficiency ranking in the year 2020 are listed in Table 6. DMU11 ranked first, having the highest efficiency score of 2.2826, with a confidence interval of (97.5-2.50%) 3.293 and 1.586 for predictive performance. The DMU14 ranked second, with a confidence interval (97.5-2.50%) of 2.675 and 0.363, and the average efficiency remaining at 1.635. DMU16 ranked third, while DMU17 ranked fourth, with the average efficiencies remaining at 1.459 and 1.441, respectively. The other three DMUs (DMU4, DMU5, DMU6) had low efficiency scores between 0.392-0.441. DMU4 was ranked last.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **TA** & **OE** & **RD** & **EP** & **REV** & **GP** \\ \hline TA & 1 & 0.988 & 0.989 & 0.975 & 0.996 & 0.991 \\ OE & 0.988 & 1 & 0.975 & 0.982 & 0.993 & 0.981 \\ RD & 0.989 & 0.975 & 1 & 0.957 & 0.982 & 0.973 \\ EP & 0.975 & 0.982 & 0.957 & 1 & 0.98 & 0.968 \\ Rev & 0.996 & 0.993 & 0.982 & 0.98 & 1 & 0.993 \\ GP & 0.991 & 0.981 & 0.973 & 0.968 & 0.993 & 1 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Average of Pearson correlation coefficients of inputs and outputs from 2015 to 2019.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**5000 Replica**} & \multicolumn{3}{c}{**500 Replica**} & \multicolumn{3}{c}{**Difference**} \\ \cline{2-10}
**DMU** & **97.50\%** & **DEA** & **2.50\%** & **97.50\%** & **DEA** & **2.50\%** & **97.50\%** & **2.50\%** \\ \hline DMU1 & 1.151 & 0.645 & 0.465 & 1.154 & 0.645 & 0.458 & 0.003 & \(-\)0.007 \\ DMU2 & 1.106 & 1.051 & 0.569 & 1.107 & 1.051 & 0.554 & 0.001 & \(-\)0.015 \\ DMU3 & 1.2 & 0.737 & 0.554 & 1.219 & 0.737 & 0.542 & 0.019 & \(-\)0.012 \\ DMU4 & 0.57 & 0.374 & 0.267 & 0.585 & 0.374 & 0.269 & 0.015 & 0.002 \\ DMU5 & 1.131 & 0.409 & 0.291 & 1.152 & 0.409 & 0.271 & 0.021 & \(-\)0.020 \\ DMU6 & 0.599 & 0.445 & 0.328 & 0.578 & 0.445 & 0.322 & \(-\)0.021 & \(-\)0.006 \\ DMU7 & 1.072 & 0.657 & 0.467 & 1.042 & 0.657 & 0.456 & \(-\)0.030 & \(-\)0.012 \\ DMU8 & 1.252 & 0.931 & 0.549 & 1.284 & 0.931 & 0.526 & 0.032 & \(-\)0.023 \\ DMU9 & 0.591 & 0.539 & 0.443 & 0.595 & 0.539 & 0.434 & 0.005 & \(-\)0.008 \\ DMU10 & 1.253 & 1.121 & 0.526 & 1.235 & 1.121 & 0.512 & \(-\)0.018 & \(-\)0.014 \\ DMU11 & 3.293 & 2.104 & 1.586 & 3.169 & 2.104 & 1.569 & \(-\)0.124 & \(-\)0.017 \\ DMU12 & 1.176 & 1.043 & 0.562 & 1.171 & 1.043 & 0.568 & \(-\)0.005 & 0.006 \\ DMU13 & 1.398 & 1.196 & 0.855 & 1.387 & 1.196 & 0.812 & \(-\)0.011 & \(-\)0.044 \\ DMU14 & 2.675 & 1.705 & 0.365 & 2.664 & 1.705 & 0.365 & \(-\)0.011 & 0 \\ DMU15 & 1.441 & 0.692 & 0.392 & 1.404 & 0.692 & 0.393 & \(-\)0.037 & 0.002 \\ DMU16 & 2.31 & 1.4 & 1.144 & 2.25 & 1.4 & 1.127 & \(-\)0.060 & \(-\)0.018 \\ DMU17 & 1.875 & 1.381 & 0.541 & 1.901 & 1.381 & 0.539 & 0.026 & \(-\)0.002 \\ DMU18 & 1.252 & 0.529 & 0.351 & 1.282 & 0.529 & 0.353 & 0.03 & 0.002 \\ DMU19 & 1.14 & 0.777 & 0.47 & 1.151 & 0.777 & 0.455 & 0.011 & \(-\)0.015 \\ DMU20 & 1.095 & 0.731 & 0.51 & 1.093 & 0.731 & 0.513 & \(-\)0.002 & 0.004 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparisons of 5000 and 500 replicas (Fisher 95%) for the period of 2015 to 2019.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Lower Bounds**} \\ \cline{2-7}  & **TA** & **OE** & **RD** & **EP** & **REV** & **GP** \\ \hline  & TA & 0.972 & 0.972 & 0.936 & 0.99 & 0.987 \\  & OE & 0.9958 & & 0.937 & 0.961 & 0.984 & 0.971 \\ Upper & RD & 0.9958 & 0.99 & 0.893 & 0.954 & 0.938 \\ bounds & EP & 0.9902 & 0.994 & 0.983 & 0.949 & 0.925 \\  & Rev & 0.9984 & 0.998 & 0.993 & 0.992 & & 0.989 \\  & GP & 0.998 & 0.996 & 0.99 & 0.988 & 0.998 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Lower/upper bounds of Fisher 95% confidence for the correlation matrix.