## 3 Empirical Results
### Forecasting Value of Inputs and Outputs Over the Period 2018-2022  
To predict the realistic input and output factors of 24 companies in Vietnam across the period 2018-2022, the GM (1,1) model is applied. Historical data of each DMU from 2013 to 2017 are used as the base to generate forecasting data for the year 2018 to 2022, respectively.  
After conducting the G (1,1) model, the forecasted data for 24 DMUs for future period 2018-2022 are obtained. However, due to limited space, we only give the result of the sample year 2018 in Table 3, below. Forecast inputs and outputs for period 2018-2022 will then be used to obtain the efficiency score for the future period.  
Forecasting always comes with error; therefore; the accuracy of the forecast model is a big concern. Thus, before using the forecasted inputs and outputs to obtain the efficiency score during period 2018-2022, it is necessary to test the accuracy of GM (1,1) model.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**DMUs** &
\begin{tabular}{c} **(I) Cost of** \\ **Goods sold** \\ \end{tabular} & **(I) Operation Cost** & **(I) Total Asset** & **(O) Profit after Tax** & **(O) Net Sales** \\ \hline DMU1 & 35,545,961 & 8,458,393 & 28,522,048 & 4,684,182 & 46,638,793 \\ DMU2 & 4,581,873 & 3,231,391 & 10,003,021 & 1,233,597 & 2,214,997 \\ DMU3 & 2,144,791 & 400,159 & 4,644,791 & 111,446 & 2,307,162 \\ DMU4 & 4,902,785 & 568,980 & 3,718,693 & 345,664 & 5,728,607 \\ DMU5 & 1,732,966 & 216,599 & 483,538 & 44,577 & 1,945,449 \\ DMU6 & 793,632 & 150,645 & 1,093,449 & 63,356 & 1,003,022 \\ DMU7 & 1,898,474 & 234,635 & 2,160,973 & 40,518 & 2,179,788 \\ DMU8 & 757,294 & 155,604 & 1,858,850 & 137,449 & 1,161,408 \\ DMU9 & 222,194 & 71,249 & 182,494 & 35,734 & 330,740 \\ DMU10 & 6,852,050 & 84,239 & 919,411 & 288,970 & 6,625,740 \\ DMU11 & 513,322 & 108,562 & 691,340 & 101,177 & 709,044 \\ DMU12 & 1,763,870 & 156,816 & 1,763,612 & 16,068 & 1,913,734 \\ DMU13 & 318,597 & 79,747 & 246,659 & 13,297 & 411,215 \\ DMU14 & 640,209 & 41,366 & 564,976 & 21,065 & 685,160 \\ DMU15 & 21,761 & 2379 & 168,088 & 2,647 & 27,085 \\ DMU16 & 347,595 & 47,240 & 523,858 & 13,047 & 397,469 \\ DMU17 & 132,776 & 42,199 & 188,963 & 4500 & 175,565 \\ DMU18 & 873,910 & 98,506 & 364,820 & 11,964 & 981,160 \\ DMU19 & 36,928 & 2371 & 140,121 & 2,552 & 40,824 \\ DMU20 & 401,577 & 30,792 & 315,140 & 7384 & 436,679 \\ DMU21 & 246,488 & 115,840 & 127,236 & 10,585 & 373,222 \\ DMU22 & 400,952 & 18,824 & 247,987 & 10,337 & 427,404 \\ DMU23 & 60,262 & 6937 & 123,085 & 1,590 & 69,728 \\ DMU24 & 480,974 & 45,792 & 443,728 & 9641 & 538,153 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Forecasted value of inputs and outputs in 2018.  
In this study, the simple but widely used testing method called mean absolute percent error (MAPE) is applied to test the error percentage of the forecast model.  
MAPE is the average absolute percent error that measures the accuracy in a fitted time series value in statistics, specifically trending.  
\[MAPE=\frac{1}{n}\sum\frac{|Actual-Forecast|}{Actual}\times 100\% \tag{20}\]  
The parameters of MAPE state the forecasting ability as following:  
MAPE \(<\) 10% represents Excellent  
10% \(<\) MAPE \(<\) 20% is Good.  
20% \(<\) MAPE \(<\) 50% \"Reasonable\"  
MAPE \(>\) 50% \"Poor  
Table 4 displays the result of MAPE. As the MAPE values obtained are, mostly, smaller than 10%, it confirms that the GM (1,1) provides a good prediction accuracy in this research.