# Influencing Factors Analysis of Crude Oil Futures Price Volatility Based on Mixed-Frequency Data
## 4 Variables and Data Description
### Analysis of the Multi-factors Associative Effect
In addition, like the previous analysis, the MAEin and RMSEin parameter estimation results of the various models in the sample are not much different, and the mixed-factor model slightly outperforms the same frequency effect model. From the out-of-sample MAEout and RMSEout parameters, the mixed factor model also outperforms the same frequency effect model. Finally, according to the quantitative indicators of each model in Table 13, comparing the high and low frequency model with the model before combining, it was found that the combination of LLC, BIC and H criteria in the hybrid low-frequency and high-frequency combination model considers more different types of factors that affect crude oil price fluctuations, and contains more effective information that affects the long-term components of high-frequency volatility and therefore reflects the advantages over the same-frequency factor combination model in terms of estimation accuracy. For example, the InventoryL+Inventory V+VL+VV model is composed of the Inventory level and volatility combined effect model and the volume combined effect model. Comparing this with the InventoryL+InventoryV model and the VL+VV model, it was found that its BIC value is \(-7.0465\), lower than the other two types models of co-frequency combination effect, and its H value is \(0.017\) \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **MAEin** & **RMSEin** & **MAEout** & **RMSEout** \\ \hline InventoryL & 0.0005 & 0.0009 & 0.0003 & 0.0003 \\ OPECL & 0.0005 & 0.0009 & 0.0002 & 0.0003 \\ Occll & 0.0005 & 0.0009 & 0.0002 & 0.0002 \\ InventoryL+InventoryV & 0.0005 & 0.0009 & 0.0002 & 0.0003 \\ OPECL+OPECV & 0.0005 & 0.0009 & 0.0002 & 0.0002 \\ OECDL+OECDV & 0.0005 & 0.0008 & 0.0002 & 0.0002 \\ VL+VV & 0.0005 & 0.0009 & 0.0002 & 0.0003 \\ InventoryL+VL+VV & 0.0005 & 0.0009 & 0.0002 & 0.0002 \\ InventoryL+InventoryV++VL+VV & 0.0005 & 0.0009 & 0.0002 & 0.0002 \\ OPECL+VL+VV & 0.0005 & 0.0009 & 0.0001 & 0.0002 \\ OECDL+InventoryV++VL+VV & 0.0005 & 0.0008 & 0.0002 & 0.0002 \\ OECDL+VL+VV & 0.0005 & 0.0005 & 0.0003 & 0.0003 \\ OECDL+OECDV++VL+VV & 0.0005 & 0.0005 & 0.0001 & 0.0001 \\ \hline \hline \end{tabular} Note: MAEin: MAE in Sample; RMSEin: RMSE in Sample; MAEout: MAE out Sample; RMSEout: RMSE out Sample.  
\end{table} 
Table 12: Comparison between the associative effect model of high-frequency and low-frequency factors and single-factor effect model. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model** & **BIC** & **LLH** & **H** & **MAE** & **RMSE** \\ \hline InventoryL & \(-7.044\) & \(-4973.91\) & 0.0182 & 0.0005 & 0.0008 \\ OPECL & \(-7.035\) & \(-4967.55\) & 0.0195 & 0.0005 & 0.0009 \\ OECDL & \(-7.0398\) & \(-4970.94\) & 0.0195 & 0.0005 & 0.0009 \\ InventoryL+InventoryV & \(-7.0387\) & \(-4977.43\) & 0.0182 & 0.0005 & 0.0008 \\ OECDL+OPECV & \(-7.032\) & \(-4972.67\) & 0.0185 & 0.0005 & 0.0009 \\ OecdL+OECDV & \(-7.0304\) & \(-4971.56\) & 0.0182 & 0.0005 & 0.0009 \\ VL+VV & \(-7.0446\) & \(-4976.48\) & 0.0172 & 0.0005 & 0.0009 \\ InventoryL+VL+VV & \(-7.0537\) & \(-4983.881\) & 0.0171 & 0.0005 & 0.0008 \\ InventoryL+InventoryV++VL+VV & \(-7.0465\) & \(-4973.03\) & 0.0170 & 0.0005 & 0.0008 \\ OECDL+VL+VV & \(-7.0537\) & \(-4983.87\) & 0.0168 & 0.0005 & 0.0008 \\ OPECL+InventoryV++VL+VV & \(-7.0326\) & \(-4973.12\) & 0.0169 & 0.0005 & 0.0008 \\ OECDL+VL+VV & \(-7.0337\) & \(-4993.874\) & 0.0172 & 0.0005 & 0.0008 \\ OECDL+OECDV++VL+VV & \(-7.1299\) & \(-6074.294\) & 0.0176 & 0.0004 & 0.0008 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Predicted parameter estimation results for each model. which is also lower than the other two models of cofrequency combination effect. It can be seen that the combined effect model, which combines two different factors of low frequency and high frequency, outperforms the model that only considers the combined effect of the same frequency factors. The comparison results of other models are basically the same, so they are not repeated here.