## 3 Multi-Dimensional Fusion Feature-Enhanced Prediction Method
### Data Augmentation of Multi-Dimensional Feature Engineering
#### 3.1.4 Cross-Variety Linkage Characteristics  
Crude oil and hot-rolled coil are different types of futures, but they are related to each other in the macroeconomic environment and industrial chain. There may be mutual influence and synergistic change between their prices. Incorporating cross-variety linkage traits can enhance the information input for the predictive model, thereby boosting its flexibility in handling a complex market landscape.  
(1) Price ratio characteristics  
To calculate the ratio of the closing price of crude oil to hot-rolled coil (_PriceRatio_), the calculation formula is as follows:  
\[PriceRatio=\frac{P_{oil}}{P_{rb}}. \tag{12}\]  
Among them, _Poil_ represents the closing price of crude oil, and _Prb_ represents the closing price of hot-rolled coil. The ratio can reflect the relative strength of the prices of the two varieties. When the price ratio rises, it shows that the price of crude oil rises faster than that of hot-rolled coil. On the contrary, it shows that the price of hot-rolled coil is relatively strong. By monitoring the change in price ratio, we can find the price linkage trend and the change in relative value between the two varieties and provide reference for predicting the price trend.  
(2) Rolling correlation characteristics  
The rolling window for calculating the yield of crude oil and hot-rolled coil is 20 (\(RollingCorr\)), and the calculation formula is as follows:  
\[RollingCorr_{t}=corr(Returns_{oil}[t-19:t],\ Returns_{rb}[t-19:t]). \tag{13}\]  
Among them, \(Returns_{oil}\) represents the yield sequence of crude oil, \(Returns_{rb}\) represents the yield sequence of hot-rolled coil, and \(corr\) represents the function of calculating the correlation coefficient (such as Pearson correlation coefficient, etc.). The correlation attributes can gauge the level of synchronization in price movements between the two commodities. A high correlation indicates that these commodities exhibit a strong alignment in their price changes, potentially influenced by shared macroeconomic elements or market sentiments. When the correlation is low or changes, it may indicate changes in market structure or influencing factors, which is of great significance for predicting price trends and risk assessment.  
(3) Price difference characteristics  
To calculate the difference between the closing price of crude oil and hot-rolled coil (\(PriceSpread\)), the calculation formula is as follows:  
\[PriceSpread=P_{oil}-P_{rb}. \tag{14}\]  
The variation in the price gap mirrors the shift in the price discrepancy between the two types. In specific market circumstances, this gap might stay within a defined fluctuation band. Should the gap veer from its typical bounds, it could instigate arbitrage activities, thereby driving the prices back to a balanced state. Consequently, the attributes of this gap are crucial for forecasting price movements and unearthing arbitrage prospects.  
(4) Trading volume ratio characteristics  
Calculate the \(VolumeRatio\) of crude oil to hot-rolled coil. The calculation formula is as follows:  
\[VolumeRatio=\frac{Volume_{oil}}{Volume_{rb}}. \tag{15}\]  
Among them, \(Volume_{oil}\) represents the volume of crude oil, and \(Volume_{rb}\) represents the volume of hot-rolled coil. The trading volume ratio can reflect the relative relationship between the two varieties in the market trading activity. When the volume ratio changes, it may mean that the distribution of market funds between the two varieties changed, which may affect the trend of price fluctuations. For example, if the volume ratio of crude oil rises suddenly, it may indicate that there will be a large price change in the crude oil market.