# 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
#### 5.4.2 Comparison of Estimation Accuracy between GARCH and GARCH-MIDAS Models  
Furthermore, in order to compare the difference in estimation accuracy between GARCH and GARCH-MIDAS-t models, the GARCH-MIDAS level and volatility effect combined model was compared with the GARCH model.  
Firstly, according to the GARCH model estimation results of the combined effect of volume level and volatility, the MAE and RMSE values were calculated; then according to the estimated value of the corresponding GARCH-MIDAS-t model, divide the MAE (RMSE) based on the GARCH-MIDAS-t model by the MAE (RMSE) of the GARCH model of the same sample to calculate RMAE (relative ratio value of MAE) and RRMSE (relative ratio value of RMSE),which can be used as the inspection index. When the RMAE (RRMSE) value is less than 1, it means that the GARCH-MIDAS model has the effect of improving the accuracy of model prediction and estimation compared with the GARCH (1,1) model.  
According to the calculation results (Table 16), the RMAE and RRMSE values of trading volume, open interest, dollar index, natural gas price, and crude oil spot price are all less than 0.05. It shows that the GARCH-MIDAS-t model, compared with the GARCH model, has a very obvious role in improving the accuracy of prediction and estimation, which reflects the advantages of the mixed frequency model compared to the same frequency model.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Variables**} & \multicolumn{2}{c}{**GARCH Model**} & \multicolumn{2}{c}{**GARCH-MIDAS Model**} & \multirow{2}{*}{**RMAE**} & \multirow{2}{*}{**RRMSE**} \\ \cline{2-2} \cline{5-7}  & **MAE** & & & & & \\ \hline V & 0.015042 & 0.021219 & 0.0005 & 0.0009 & 0.032131 & 0.041224 \\ OI & 0.015040 & 0.021213 & 0.0005 & 0.0008 & 0.031542 & 0.03938 \\ DI & 0.015040 & 0.021217 & 0.0005 & 0.0008 & 0.031299 & 0.039288 \\ GP & 0.015041 & 0.021218 & 0.0005 & 0.0009 & 0.032129 & 0.041074 \\ PS & 0.015069 & 0.021229 & 0.0005 & 0.0008 & 0.030623 & 0.03846 \\ \hline \hline \end{tabular}
\end{table}
Table 16: RMAE and RRMSE values of GARCH model and GARCH-MIDAS model.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Variable** & \multicolumn{2}{c}{**GARCH Model**} & \multicolumn{2}{c}{**GARCH-MIDAS Model**} \\ \hline  & **Level Effect** & \multicolumn{2}{c}{**Volatility Effect**} & \multicolumn{2}{c}{**Level Effect**} & \multicolumn{2}{c}{**Volatility Effect**} \\ \cline{2-7}  & **Correlation** & **Significance** & **Correlation** & **Significance** & **Correlation** & **Significance** & **Correlation** & **Significance** \\ \hline V & + & *** & + & + & *** & + & *** \\ OI & – & *** & + & *** & + & + & + \\ DI & + & ** & + & *** & + & + & ** \\ GP & + & + & + & + & + & + & *** \\ PS & – & *** & + & *** & – & + & ** \\ \hline \hline \end{tabular} Note: + and – indicate positive correlation and negative correlation, respectively; *, **, *** mean statistically significant at the significance level of 10%, 5%, and 1%, respectively.  
\end{table}
Table 15: Comparison of estimation results between GARCH model and GARCH-MIDAS model.