# Exploiting Deep Learning for Wind Power Forecasting Based on Big Data Analytics
## 7 Results and Analysis
### Statistical Analysis of EDCNN  
The aforementioned error indicator (Table 3) were utilized for accuracy comparison of forecasting models. However, the lesser error or higher accuracy of a model does not guarantee its superiority over other models. A model is better as compared to another model if the difference between their accuracies is statistically significant. Different statistical tests are used to validate the significance of models, such as error analysis [49], [PERSON] test [50], Diebold-Mariano (DM) test [51], etc. To validate the performance of the proposed forecasting model EDCNN, a well-known statistical test, DM, was used. [PERSON] and [PERSON] proposed the classical Diebold-Mariano statistical test in 1995 [51]. The DM test evaluates the significant difference between forecasting errors to two models. The null hypothesis \(H_{0}\) states that the models have equal accuracy (when the value of \(d_{t}^{FM^{1},\ FM^{2}}\) in Equation (18) is equal to zero). The alternative hypothesis \(H_{1}\) is that one model is significantly more accurate as compared to the other mode (if the value of \(d_{t}^{FM^{1},\ FM^{2}}\) in Equation (18) is greater than zero, Model 1 is better than Model 2).  
A vector of values that are to be forecasted are \(X=[X_{1},\ X_{2},\ \ldots,\ X_{n}]\). Two prediction models \(FM\) predict these values, i.e., \(FM^{1}\) and \(FM^{2}\). The forecasting errors of these models are:  
\[\varepsilon^{FM^{1}} = [\varepsilon_{1}^{FM^{1}},\ \varepsilon_{2}^{FM^{1}},\ \ldots,\ \varepsilon_{n}^{FM^{1}}]\] \[\varepsilon^{FM^{2}} = [\varepsilon_{1}^{FM^{2}},\ \varepsilon_{2}^{FM^{2}},\ \ldots,\ \varepsilon_{n}^{FM^{2}}]\]  
In this study, the error metric used for DM is MAE. A covariance loss function \(L(\cdot)\) and differential loss was calculated in DM as Equation (18) [52]:  
\[d_{t}^{FM^{1},\ FM^{2}}=L(\varepsilon_{t}^{FM^{1}})-L(\varepsilon_{t}^{FM^{2}}) \tag{18}\]  
DM is widely used for validation of wind power forecasting [53]. The results of the DM test with confidence level of 95% are shown in Table 4. DM was applied to the forecasting results of EDCNN and two compared methods: CNN and SELU CNN [37]. Three comparisons were performed, i.e., EDCNN with CNN, EDCNN with SELU CNN and CNN with SELU CNN. The EDCNN was better than CNN and SELU CNN was better than CNN. The DM and \(p\)-values are shown in Table 4).  
The significance level of \(p\)-value is 5%. In the comparison of EDCNN and SELU CNN, the \(d_{t}^{FM^{1},\ FM^{2}}\) value is more than zero, which depicts that the EDCNN model is significantly better than SELU CNN and similarly EDCNN is better than CNN. According to the DM's hypothesis \(H_{1}\), if the DM value is greater than zero, the first model is significantly better than the second model. The results in Table 4 show that the forecasting accuracy of EDCNN is significantly better than SELU CNN and CNN. SELU CNN is significantly better than CNN.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **Season** & **MAPE** & **NRMSE** & **MAE** \\ \hline \multirow{4}{*}{CNN} & Spring & 8.42 & 2.34 & 3.34 \\  & Summer & 8.23 & 2.27 & 3.24 \\  & Autumn & 7.9 & 2.65 & 3.36 \\  & Winter & 8.1 & 2.71 & 2.89 \\ \hline \multirow{4}{*}{SELU CNN} & Spring & 3.47 & 0.12 & 3.1 \\  & Summer & 3.62 & 0.13 & 3.3 \\  & Autumn & 3.45 & 0.12 & 3.4 \\  & Winter & 3.27 & 0.17 & 3.2 \\ \hline \multirow{4}{*}{EDCNN} & Spring & 2.67 & 0.092 & 2.4 \\  & Summer & 2.43 & 0.096 & 2.24 \\ \cline{1-1}  & Autumn & 2.56 & 0.085 & 2.67 \\ \cline{1-1}  & Winter & 2.62 & 0.094 & 2.18 \\ \hline \hline \end{tabular}
\end{table}
Table 3: MAPE and NRMSE of proposed and compared methods.