# Influencing Factors Analysis of Crude Oil Futures Price Volatility Based on Mixed-Frequency Data
## 4 Variables and Data Description
### Data Processing and Basic Characteristic Analysis  
#### 4.2.1 Interpreted Variables  
The rate of return of oil futures prices selects the logarithmic rate of return \(RF\), that is, the logarithm of the current oil futures price minus the logarithm of the previous period's futures price. The calculation formula is  
\[RF_{t}=lnPF_{t}-lnPF_{t-1} \tag{21}\]  
where \(PF_{t}\) represents the Brent crude oil futures price on day \(t\); \(PF_{t-1}\) represents the Brent crude oil futures price on day \(t\)-1. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  
It can be seen from Figure 1 that the trend of Brent crude oil futures prices and spot prices are almost the same, showing good consistency. From January 2008 to July 2008, the Brent crude oil futures price and the spot price were in the rising range and reached the highest point in history. From August 2008 to March 2009, they were in a downward trend. By July 2014, it entered the turbulent rise range, and then gradually fell, and rebounded after the end of 2017. It can be seen from Figure 2 that the volatility of the Brent crude oil futures price yield shows a \"clustering\" phenomenon, and the volatility was small over a period of time, such as the data from 2013 to 2014, and it was very large in some time periods, such as year 2008 to 2009, and year 2015 to 2016. Judging from the basic statistical characteristics of each series in Table 2:  
1 The average value of Brent crude oil futures returns is negative. In other words, for a long futures investor, the average investment income during the sample period is negative. In fact, if the transaction costs (such as transaction fees, the cost of funds occupied by margin, etc.) are considered, the futures yield is even lower. Obviously, the average value of Brent crude oil spot and futures price series is greater than zero. 2 Nonnormality of sequence distribution. A common assumption in financial theory and empirical analysis is that the rate of return obeys a normal distribution. However, the actual financial rate of return often obeys a nonnormal distribution. The Brent crude oil futures prices, spot prices, and futures returns are no exception, the statistics in Table 2 illustrate this point. The skewness of the normal distribution should be equal to 0, that is positive skewness while the skewness value of the Brent crude oil futures return series is greater than 0, and that is negative skewness while the skewness of the Brent crude oil futures price and spot price series is less than 0. The kurtosis of spot prices and futures prices is less than 3, while the kurtosis of the Brent crude oil futures return sequence is greater than 3, indicating that it is a kurtosis distribution and fat-tailed distribution. The thick-tailed distribution means that there are many sample values that deviate from the sample average by a large margin, that is, the absolute value of the rate of return is larger than expected. If the rate of return is normally distributed, then the Q-Q chart should be a straight line. In fact, the Q-Q diagram is an S-shaped curve, which shows that it has the characteristics of sharp peaks  
Figure 1: Trend chart of Brent crude oil futures price and spot price. and thick tails compared to the normal distribution. The test statistics of JB (Jarque-Bera) for all series are also much larger than the critical value (5.992). Based on the above results, it can be seen that the sequence has the characteristics of sharp peaks and thick tails, and does not obey the normal distribution. From the perspective of coefficient of variation (CV), the volatility of Brent crude oil spot prices is slightly higher than that of futures prices. In addition, because the mean value of Brent crude oil futures returns is negative, its CV value is less than zero, but the absolute value of CV is relatively large, indicating that the fluctuations are relatively severe. Then, we will further discuss the basic statistical characteristics of Brent crude oil futures prices, spot prices, and futures yields.