# Influencing Factors Analysis of Crude Oil Futures Price Volatility Based on Mixed-Frequency Data
## 4 Variables and Data Description
### Analysis of the Single-Factor Associative Effect of Level and Fluctuation
#### 5.2.2 Analysis of the Combined Effect of High-Frequency Variables
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Variable** & **V** & **OI** & **DI** & **GP** & **PS** \\ \hline \(\mu\) & 0.0001 & 0 & 0 & 0.0024 ** & 0 \\  & [0.9645] & [0.9494] & [0.9341] & [0.0362] & [0.9323] \\ \(\alpha\) & 0.9056 *** & 0.0421 & 0.0425 *** & 0.8181 *** & 0.0412 *** \\  & [0] & [0.6607] & [0] & [0.0006] & [0] \\ \(\beta\) & 0.0940 & 0.9554 *** & 0.9549 *** & 0.1375 & 0.9563 *** \\  & [0.4174] & [0] & [0] & [0.5845] & [0] \\ \(m\) & 0.2121 & \(-9.4252\) & \(-9.4256\) *** & \(-0.6886\) *** & \(-9.4259\) *** \\  & [0.9995] & [0.6304] & [0] & [0] & [0] \\ \(\theta_{l}\) & 0.0212 *** & 0.8479 & 0.2187 & 0.0033 *** & \(-0.2594\) \\  & [0] & [0.9649] & [0.6479] & [0] & [0.7957] \\  & 2.5393 *** & 0.9963 & 0.9693 ** & 0.0239 *** & 0.9918 ** \\ \(\theta_{v}\) & [0] & [0.9512] & [0.0332] & [0] & [0.0137] \\ \(\omega_{l}\) & 1.0989 * & 17.8177 & 10.5885 *** & 7.2627 *** & 10.6961 *** \\  & [0.0591] & [0.1411] & [0] & [0] & [0.0000] \\ \(\omega_{v}\) & 9.9031 & 19.9077 & 19.1271 *** & 7.8873 *** & 19.6052 *** \\  & [0.5319] & [0.5599] & [0] & [0] & [0] \\  & 3.3383 & 0.9212 & 0.8993 & 5.8090 & 0.9011 * \\  & [0.7190] & [0.9578] & [0.1889] & [0.7427] & [0.0897] \\ \(\eta\) & 6.4362 & 6.4633 & 6.4302 & 6.4376 & 6.4605 \\  & [0] & [0.1868] & [0] & [0] & [0] \\  & \(-0.0406\) & \(-0.0397\) & \(-0.0402\) & \(-0.0395\) & \(-0.0394\) \\ \(\lambda\) & [0.2091] & [0.3299] & [0.2148] & [0.2207] & [0.2214] \\ BIC & \(-7.0446\) & \(-7.0331\) & \(-6.9999\) & \(-7.0323\) & \(-7.0339\) \\ LLH & \(-4976.48\) & \(-4973.49\) & \(-5020.22\) & \(-6772.94\) & \(-4977.61\) \\ H & 0.0172 & 0.0175 & 0.0199 & 0.0182 & 0.0182 \\ MAE & 0.0005 & 0.0005 & 0.0005 & 0.0005 & 0.0005 \\ RMSE & 0.0009 & 0.0008 & 0.0008 & 0.0009 & 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 9: Estimation results of associative model of level and fluctuation effect in high-frequency factors. of DI is significant in the portfolio analysis, indicating that the correlation between the fluctuation of the US dollar index and the fluctuation of crude oil is enhanced after combining the level of the US dollar index. Changes in the exchange rate of the US dollar will cause fluctuations in the nominal price of crude oil, thereby increasing the volatility of crude oil futures. Whether it is a layered analysis or a combination effect analysis, the volatility effect of spot prices is always significantly positive, reflecting the close connection and linkage between the Brent crude oil futures market and the spot market. Based on the results of the hierarchical analysis and combination analysis of high-frequency factors, both high-frequency on-market and off-market factors are important factors in the volatility of international crude oil futures returns, especially the on-market trading volume of the high-frequency factor, the off-market natural gas price, and the crude oil spot price of the high-frequency factor.