## 5 Comparison of Forecasting Results by Different Forecasting Models  
With the aim of evaluating the precision of Rolling-MFO-GM (1,1) model for annual electricity consumption forecasting, the LSR (least square regression) method, GM (1,1), FOA (fruit fly optimization)-GM (1,1), MFO-GM (1,1), Rolling-LSR, Rolling-GM (1,1) and Rolling-FOA-GM (1,1) are selected as the compared models. Among these models, LSR method, GM (1,1), FOA-GM (1,1) and MFO-GM (1,1) are a class of forecasting models without rolling mechanism, while Rolling-LSR, Rolling-GM (1,1), Rolling-FOA-GM (1,1) and Rolling-MFO-GM (1,1) are another class of forecasting models with rolling mechanism. Specifically, LSR method, which is not a grey-based forecasting technique, is selected to validate the effectiveness of the proposed approach. As the most well-known linear model in statistics and mathematics, LSR method is an effective technique to realize correlation analysis between variables. Given a set of training samples, LSR can find the coefficients of a linear model by minimizing the residual sum of squares [57]. For LSR method, the electricity consumption data points from 2001 to 2009 of Inner Mongolia will be treated as the training samples. The regression coefficient \(a\) and constant term \(b\) are shown in Table 2. According to the regression model, the forecasting values can be obtained (see Table 3). For GM (1,1), the input data sequence is the electricity consumption data from 2001 to 2009 of Inner Mongolia, and then the parameters \(a\) and \(b\) can be determined (see Table 2). On the basis of this, the forecasting results of 2010-2014 can be calculated using Equation (13) (see Table 3). For FOA-GM (1,1), the optimization algorithm FOA is applied to iteratively select the optimal value of parameters \(a\) and \(b\) of GM (1,1). Before iteration, the original parameters of FOA are set as follows: _maxgen_ = 100, _sizepop_ = 20, (_X_axis_, _Y_axis_) \(\subset\) [- 50, 50], FR \(\subset\) [- 10, 10], _X_axis_ = rands \((1,2)\), _Y_axis_ = rands \((1,2)\). The values of parameters \(a\) and \(b\) optimized by FOA are listed in Table 2, and the prediction results are shown in Table 3.  
For MFO-GM (1,1), the forecasting procedure is shown as Figure 4. Applying the electricity consumption from 2001 to 2009 as input sequence, the parameters \(a\) and \(b\) can be optimized by MFO. Before iteration, the initial parameters setting are same as that in Section 3.2. Then, we can use the optimal values of \(a\) and \(b\) which are itemized in Table 2 to calculate the electricity consumption of 2010-2014, and the results are shown in Table 3.  
For Rolling-LSR, we can obtain five regression models using five groups of data sequence. The electricity consumption from 2001 to 2009 are treated as the input sequence of LSR, so the electricity consumption of 2010 can be calculated based on the first regression model. Then, the data from 2002 to 2010 are employed as input sequence, so the electricity consumption of 2011 can be forecasted on the basis of the second regression model, and so on. Finally, five regression models can be obtained, and the electricity consumption from 2010 to 2014 can be forecasted, which are shown in Table 3. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Year**} & \multicolumn{2}{c}{**Parameters**} & \multirow{2}{*}{**Forecasting Value**} & \multirow{2}{*}{**Actual Value**} & \multirow{2}{*}{**The Gap**} \\ \cline{2-2} \cline{5-6}  & \(a\) & \(b\) & & & \\ \hline
2010 & \(-\)0.2137 & 241.6629 & 1546.38 & 1536.83 & \(-\)9.55 \\
2011 & \(-\)0.1774 & 349.1043 & 1881.12 & 1864.07 & \(-\)17.05 \\
2012 & \(-\)0.1711 & 444.6820 & 2189.21 & 2016.76 & \(-\)172.45 \\
2013 & \(-\)0.1416 & 629.6003 & 2315.54 & 2068.01 & \(-\)247.53 \\
2014 & \(-\)0.1341 & 750.4858 & 2462.04 & 2251.05 & \(-\)210.99 \\ \hline \hline \end{tabular} The gap means the different between the forecasting value and actual value. Of which, the negative value indicates the forecasting value is larger than the actual value.  
\end{table}