# High-Frequency Direction Forecasting of the Futures Market Using a Machine-Learning-Based Method
## 5 Results and Discussion
### Results of LIME  
In the proposed method, the LIME algorithm is applied to interpret how the XGBoost made multiclassification of the rebar futures price direction. Since the proposed method produced the largest accumulated return during the third period, the LIME results within the third period are presented and discussed. The effects of each variable on the multiclassification results for the sample in the third period are illustrated in Figure 6. The subplots (a)/(b)/(c)/(d) represent the prediction results for label = 1/2/4/5, respectively. Note that label = 3 indicates no trading. In addition, these labels correspond to four trading signals. The horizontal axis of each subplot contains the ten cases we selected in the testing period, while the vertical axis of each subplot displays the influence of features on the prediction results. Additionally, a red square means that the feature has a negative influence, while a blue one reflects a positive influence. A deeper color means that it is more influential of that feature. Note that we focus on the top eight most important features out of all features. As we explained in Section 4.1, Ri (\(Return_{i}\)), Ti (\(TVCR_{i}\)), and Ii (\(OICR_{i}\)) respectively, denote the return at time \(i\), trading volume change rate at time \(i\), and open interest change rate with lag length \(i\). For example, \"I02\" represents the open interest change rate with a lag of two periods.  
In Figure 6a, it can be observed that for case 1, the top eight most influential features for the prediction result \"label = 1\" are \"I01\", \"I03\", \"R02\", \"R07\", \"R08\", \"T02\", \"T04\", and \"T09\". Among them, when feature R07 is larger than 0.558 and feature R08 exceeds to 0.559, they both have a positive influence on the classification results. When feature \"I01\" is larger than 0.737 and less than 0.777, feature \"I03\" is larger than 0.737 and less than 0.777.  
Figure 5: The relative importance of input features for the proposed method in four training periods.  
Figure 6: The LIME explanation results for the prediction cases 1–10. The sub-figures **(a–d)** are the explanation results for labels 1/2/3/4.  
than 0.778, feature \"R02\" is larger than 0.491 and less than \"0.563\", feature \"T02\" exceeds 0.01535, feature \"T04\" exceeds 0.00159, and feature \"T09\" exceeds 0.01508, then they all have negative effects on the prediction results. Moreover, it is obvious that features \"T02\" and \"T09\" exert greater influence on the results in the range compared to other features with negative influence. Similar conclusions can be drawn from other cases. In general, for the result \"label = 1\", there is a great negative influence when feature \"I04\" is larger than 0.776 and \"T02\" is larger than 0.01535. Additionally, there is a significant positive effect as feature \"R07\" exceeds 0.558 and \"R08\" exceeds 0.559; Similarly, for \"label = 2\", there is a significant negative effect as feature \"T01\" exceeds 0.01534 and a significant positive effect when feature \"T09\" exceeds 0.01508; for \"label = 4\", there is a significant positive effect as feature \"R05\" exceeds 0.559; for \"label = 5\", when feature \"I03\" exceeds 0.778 and features \"I04\" and \"I05\" exceed 0.776, there is a significant positive effect on the classification results. On the contrary, there is a significant negative effect when \"R05\" exceeds 0.559. The model explanation using LIME effectively enhanced the interpretability of the proposed approach. It provides market investors and regulators with a powerful tool to better understand how the proposed method makes predictions and trading.