## 2 Data Analysis and Preprocessing
### Correlation Analysis of Historical Data  
As mentioned earlier, the wind power waveform can be observed to have strong volatility and randomness. Such data features pose difficulties for power prediction. This is because the conventional prediction algorithms for time series data sources typically involve analyzing and extracting historical data characteristics, transferring them to a neural network for computation, and ultimately achieving series prediction through regression techniques [26; 27]. However, such algorithms have high requirements for the correlation in historical data. Furthermore, the data characteristics of strong randomness and volatility are inevitable, which leads to the low correlation between the future changes in data and  
Figure 1: The chart of wind power characteristic analysis. All data are standardized by Z-Score. The sampling period is 1 h.  
historical data in a long time scale, which seriously affects the accuracy of the prediction model. In order to verify this assumption, this paper analyzes the correlation in the data.  
With the sampling frequencies of 15 min and 1 h, sampling time was 2 weeks, and the results are shown in Figure 2. If the historical data correlation graph were displayed point by point, the image would be too long and would not have a good observation effect. The folding period is in {2, 4, 8, 16} data points, and the folded data input is \(x\in\mathbb{R}^{\text{L}}\rightarrow\mathfrak{x}\in\mathbb{R}^{\text{L}/ \mathbb{N}\times\mathbb{N}}\). L is the length of the input sequence. N is the folding period. This correlation graph is more readable.  
In the image with a 15 min sampling period and a folding period of 2, it can be seen that the historical correlation in wind power data changes over time. The darker the color, the lower value, which indicates a lower correlation. Conversely, as color brightness increases, the associated values increase, signifying a higher level of historical relevance. Within the entire length range, only 4-5 time windows show high correlation. The degree of correlation is low in most other time windows. High correlation data have lower dimensions and longer lengths. As the folding period increases, the data dimension increases and the length decreases. Different folding methods can lead to data presenting different features in a spatiotemporal range, which is also an important factor affecting prediction models.  
In summary, regardless of the sampling period and folding dimension used for observation, the overall historical correlation in wind power data is relatively low. Only within a random and brief time window, a high correlation can be observed. Such data characteristics are not sufficient to support traditional deep learning models in learning historical representations, and can also bring uncertainty in prediction. While it may exhibit some efficacy in short-term forecasting, its performance diminishes significantly  
Figure 2: The chart of historical data correlation analysis. The higher the historical correlation, the brighter the image. In the opposite case, it becomes darker.  
when applied to medium- to long-term forecasting. Specific experimental results can be found in Section 5.2.2. Therefore, it is necessary to study power prediction models that are suitable for both short-term and medium- to long-term power prediction based on such data characteristics.