# Direct Multistep Wind Speed Forecasting Using LSTM Neural Network Combining EEMD and Fuzzy Entropy
## 4 The Predictable Time of Wind Speed Series
### Analysis of Predictable Time  
Because the selected wind speed series in different regions are different, the correlation length of each month's wind speed series obtained by taking MIC equal to 0.2 is also different. Therefore, this paper compared the influence of different correlation lengths on wind speed forecasting error to obtain a more general wind speed predictable length.  
In this paper, the basic time series forecasting method, Persistence Model [42], was used to forecast the corresponding correlation length of each month's wind speed series. Assuming that the wind speed series of a certain month is \(\{v(t),\,t=1,\,2,\,\ldots,\,N\}\), and the correlation length obtained when the MIC equals 0.2 is denoted by \(l\) (unit is h). Since the recorded time interval of the three anemometer towers is 10 min, the number of wind speed data with a correlation length of \(l\) is \(\delta l\). The wind speed series was segmented according to \(\delta l\), and then the wind speed of the previous period was used to forecast the wind speed of the next period. That is to say, \(\{v(t),\,t=1,\,2,\,\ldots,\,\delta l\}\) was used to forecast \(\{v(t),\,t=\delta l+1,\,\delta l+2,\,\ldots,\,2\times\delta l\}\); \(\{v(t),\,t=\delta l+1,\,\delta l+2,\,\ldots,\,2\times\delta l\}\) was used to forecast \(\{v(t),\,t=2\times\delta l+1,\,2\,\times\,\delta l+2,\,\ldots,\,3\times\delta l\}\) and so on until the end of the series.  
After using the persistence model to forecast the 36 wind speed series in different regions, the errors between the measured and forecasted wind speed of each month were counted. Mean Absolute Error (\(MAE\)) and Root Mean Squared Error (\(RMSE\)) were used as the error evaluation index. The formulas for calculating \(MAE\) and \(RMSE\) are as follows:  
\[MAE=\frac{1}{N}{\sum\limits_{i=1}^{N}}{\left|{{v_{i}}-{v_{pi}}}\right|} \tag{9}\]  
\[RMSE=\sqrt{\frac{1}{N}{\sum\limits_{i=1}^{N}}{\left({{v_{i}}-{v_{pi}}}\right) ^{2}}} \tag{10}\]  
where \(N\) is the number of forecasted wind speed data; \(v_{i}\) is the measured wind speed, m/s; \({v_{pi}}\) is the forecasted wind speed, m/s.  
The variation law of \(MAE\) and \(RMSE\) with the correlation length is shown in Figure 5. As the correlation length of the wind speed series increases, the forecasting error tends to increase overall.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Month**} & \multicolumn{3}{c}{**Correlation Length (h)**} \\ \cline{2-4}  & **Anempometer Tower 1** & **Anempometer Tower 2** & **Anempometer Tower 3** \\ \hline January & 8.17 & 6.17 & 6.67 \\ February & 5.83 & 5.83 & 3.67 \\ March & 14.83 & 4.50 & 6.83 \\ April & 7.50 & 6.00 & 4.67 \\ May & 12.50 & 4.17 & 6.17 \\ June & 4.50 & 3.67 & 4.83 \\ July & 7.00 & 3.33 & 5.33 \\ August & 3.00 & 4.00 & 8.67 \\ September & 6.33 & 3.83 & 6.67 \\ October & 9.67 & 6.00 & 5.17 \\ November & 7.67 & 6.50 & 5.00 \\ December & 9.00 & 4.17 & 8.50 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Correlation length of wind speed series when MIC equals 0.2.  
However, when the correlation length is less than four hours, the forecasting error is small and stable, and the fluctuation range is small. Therefore, four hours can be used as the predictable time of the wind speed series for direct multistep forecasting based on historical wind speed data. The forecasting time of the wind speed series in the following section was taken as four hours.