# Influencing Factors Analysis of Crude Oil Futures Price Volatility Based on Mixed-Frequency Data
## 4 Variables and Data Description
### Analysis of the Single-Factor Hierarchical Effect of Level and Fluctuation
#### 5.1.2 Single Factor Volatility Effect
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Variable** & **V** & **Oi** & **DI** & **GP** & **PS** \\ \hline \(\mu\) & 0.0001 & 0.0002 & 0.0001 & 0.0001 & 0.0001 \\  & [0.9449] & [0.2377] & [0.8790] & [0.8442] & [0.9965] \\ \(\alpha\) & 0.0332 *** & 0.3999 *** & 0.0375 & 0.0362 *** & 0.0384 *** \\  & [0] & [0] & [0.3911] & [0] & [0] \\ \(\beta\) & 0.9667 *** & 0.6000 *** & 0.9621 *** & 0.9605 *** & 0.9547 *** \\  & [0] & [0] & [0] & [0] & [0] \\ \(m\) & \(-6.5572\) *** & \(-1.0000\) & \(-8.0806\) & \(-9.5688\) *** & \(-9.2252\) *** \\  & [0] & [0.9948] & [0.9469] & [0] & [0] \\ \(\theta_{v}\) & 0.000 *** & 1.8822 & 2.6597 & 7.9867 *** & 0.0001 *** \\  & [0] & [0.9845] & [0.9825] & [0] & [0] \\ \(\omega_{l}\) & 7.8997 & 6.6237 & 5.7794 & 4.3075 & 9.3012 \\  & [0.4096] & [0.9970] & [0.9992] & [0.5402] & [0.4894] \\ \(g_{0}\) & 0.0404 ** & 1.9986 & 0.4172 & 1.8398 & 7.9645 * \\  & [0.0181] & [0.9948] & [0.9934] & [0.2056] & [0.0664] \\ \(\eta\) & 6.4305 & 6.4242 & 6.4221 & 6.4206 & 6.4223 \\  & [0] & [0] & [0] & [0] & [0] \\ \(\lambda\) & \(-0.0408\) & \(-0.0403\) & \(-0.0403\) & \(-0.0401\) & \(-0.0403\) \\  & [0.2078] & [0.2123] & [0.2115] & [0.2141] & [0.2123] \\ BIC & \(-7.0428\) & \(-7.0423\) & \(-7.0418\) & \(-6.946\) & \(-7.0423\) \\ LLH & \(-4973.02\) & \(-4972.65\) & \(-4972.32\) & \(-6774.82\) & \(-4972.69\) \\ H & 0.0173 & 0.0174 & 0.0175 & 0.0173 & 0.0188 \\ MAE & 0.0005 & 0.0005 & 0.0005 & 0.0005 & 0.0005 \\ RMSE & 0.0008 & 0.0008 & 0.0009 & 0.0008 & 0.0008 \\ \hline \hline \end{tabular} Note: ***, **, and * indicate statistically significant at the significance level of 1%, 5%, and 10%, respectively; p values are in brackets [ ].  
\end{table} 
Table 6: Estimation results of high-frequency and single-factor fluctuation effect model. 5 The increase in the volatility of crude oil inventories, crude oil consumption, crude oil production, substitute prices, and speculative factors will increase the volatility of the Brent crude oil futures market. Relatively speaking, the impact of substitutes is not sufficiently obvious. (2) Analysis of volatility effects of high-frequency variables  
The volatility effects of high-frequency variables are estimated as shown in Table 6.  
From the estimated results in Table 6, we can see the following:  
1 Similar to the low-frequency variable volatility effect model, the \(\alpha+\beta\) value of each model of the high-frequency variable volatility effect is very close to 1, indicating that each model has a relatively strong ARCH effect and relatively strong volatility persistence. In addition, the H value of the trading volume and natural gas price fluctuation effect model is 0.0173, the H value of the open interest and the dollar index fluctuation effect model is slightly higher, and the value of the spot price fluctuation effect model is the largest. Regarding LLH, the natural gas price model has the highest accuracy, but its BIC value is the largest, so from these two standards, the evaluation results are inconsistent, indicating that the stability of this model is poor. The MAE and RMSE values of each model have almost no difference. 2 In addition, based on the comparison between the high-frequency factors volatility effect model and the high-frequency factors horizontal effect model, although the corresponding models have advantages and disadvantages based on the BIC, LLH, and H criteria, the volatility model generally outperforms the level effects model. From the average value of the indicators of the five models, the BIC, LLH, and H values of the horizontal effect model are \(-\)7.0226, \(-\)5280.11, and 0.0174, and the five types of indicators of the volatility effect model are \(-\)7.0230, \(-\)5333.10, and 0.0177, respectively. Therefore, in general, the volatility effect model of high-frequency factors slightly outperforms the horizontal effect model.