## 3 Experimental Results and Discussion
### Practical Sample 3: Forecasting the Residential Electricity Consumption in Chong Qing  
In this practical sample, the total residential electricity consumption in Chong Qing is employed to construct proposed models. The evaluation of model performance is processed in the same manner as two previous samples. The sample data from 2000 to 2009 is adopted from [26]. Table 4 and Figure 3 presented the obtained results from practical sample 3. The value of _RMSE_ and _MAPE_ clearly indicated that the DGM(2,1) model turned out 11.18% for _RMSE_ and 11.44% for _MAPE_. It has larger _RMSE_ and _MAPE_ values than the MDGM(2,1) (8.31% and 9.84%), the FDGM(2,1) (3.45% and 4.27%), and the FMDGM(2,1) (2.36% and 3.25%). The precision rate of DGM(2,1) (88.56%) is low compared with the MDGM(2,1) (90.16%), FDGM(2,1) (95.72%) and the FMDGM(2,1) (96.75%) models. Consequently, the accuracy of the DGM(2,1) model is the lowest. Furthermore, with the obtained results from the data of the total residential electricity consumption in Chong Qing, we can conclude that, in all of the modified of DGM(2,1) models, the FMDGM(2,1) model has a strong forecasting performance. Figure 2: Comparison of the forecasting capability of different DGM(2,1) models for Myanmar’s inbound FDI. As noted in the introduction in Section 2.3, besides some statistical measurements, the developing coefficient, \(a\), of grey models is also used as an evaluative standard to judge the forecasting capability of the proposed models. The coefficient, \(a\), of the DGM(2,1) model for the three practical samples has been calculated and presented in Table 5. The \(a\) value of the three practical samples is \(0.18369\), \(-0.1775\) and \(-0.221\), respectively. According to the standard in Table 1, the \(a\) values of the three practice samples are placed in the first range of Table 1. This means that the DGM(2,1) model can be considered for middle and long-term forecasting (24). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Year**} & \multirow{2}{*}{**Actual Values \({}^{\ast}\)**} & \multicolumn{4}{c}{**Relative Percentage Error (\%)**} \\ \cline{3-6}  & & **DGM(2,1)** & **MDGM(2,1)** & **FDGM(2,1)** & **FMDGM(2,1)** \\ \hline
2000 & 47.91 & 0 & 0 & 0 & 0 \\
2001 & 51.02 & 4.96 & 5.13812 & 11.17 & 3.57 \\
2002 & 53.12 & 6.19 & 3.50478 & 5.78 & 1.94 \\
2003 & 48.44 & 6.31 & 16.9566 & 0.13 & 4.06 \\
2004 & 53.56 & 0.04 & 9.67076 & 0.72 & 6.50 \\
2005 & 60.9 & 7.73 & 0.72557 & 3.71 & 2.65 \\
2006 & 76.47 & 22.27 & 15.5378 & 6.23 & 3.57 \\
2007 & 74.99 & 15.34 & 8.47032 & 5.21 & 0.04 \\
2008 & 84.99 & 19.36 & 13.2951 & 0.42 & 4.13 \\
2009 & 94.41 & 20.73 & 15.2702 & 4.99 & 2.83 \\ \hline \multicolumn{6}{c}{_RMSE_} & 11.18 & 8.31 & 3.45 & 2.36 \\ \hline \multicolumn{6}{c}{_MAPE_ (\%)} & 11.44 & 9.84 & 4.27 & 3.25 \\ \hline Precision rate (\%) & 88.56 & 90.16 & 95.72 & 96.75 \\ \hline Forecasting grade & Qualified & Qualified & Good & Good \\ \hline \multicolumn{6}{c}{* Total residential electricity consumption (\(10^{8}\) kWh). Data adopted from [PERSON] _et al._[26].} \\ \end{tabular}
\end{table} 
Table 4: Forecasting results for the residential electricity consumption in Chong Qing. Figure 3: Comparison of the forecasting capability of different DGM(2,1) models for residential electricity consumption. To sum up the above analyses, based on the obtained results from the data of three practical samples, we can recognize that the accuracy of the original DGM(2,1) model is significantly low compared to the MDGM(2,1), FDGM(2,1) and FMDGM(2,1) models. The precision rate of the DGM(2,1) falls from 82.95% to 88.56%. With this value, the forecast performance of the DGM(2,1) has not yet reached a good forecasting level [23] and needs to be enhanced when directly applied to real circumstances. However, for the modified models, after correcting the residual series by utilizing the Fourier series and the Markov chain, the forecast errors of the DGM(2,1) were clearly reduced.