Forecasting China's crude oil futures volatility: New evidence from the MIDAS-RV model and COVID-19 pandemic (2024)

2.1. Prediction models

In this study, we utilize the standard MIDAS model proposed by Ghysels et al. (2007) as the benchmark model. The MIDAS-RV model can be expressed by the following equation:

where RVt=∑j=1Frt,j2,r_t,j indicates the jth intraday return at Day t and F indicates the number of observations. RVt−k−1 represents the lags t-k-1 of RV. In this paper, we choose kmax that is equal to 22. The weight b(k,θRV) can be written as follows:

where f(z,a,b)=za−1(1−z)b−1/φ(a−b) and φ(a,b) can be defined as φ(a,b)=Γ(a)Γ(b)/Γ(a+b). According to the studies of Santos and Ziegelmann (2014) and Conrad and Loch (2015), we assign the parameter θ1 of the weighting scheme to 1. Therefore, the weighted values are only dependent on the parameter θ2, which should be larger than 1 to ensure nonnegative volatilities. To investigate the role of jumps, we design the MIDAS-RV-CJ model, defined as follows:

We also consider the leverage effect of the MIDAS-RV model to design the MIDAS-RV-L model, which is given as follows:

where rt−k−=min(rt−k,0), which includes the leverage effect and is helpful to explore the impact of lagged negative returns on future China crude oil RV.

2.2. Data

We collect the 5-min high-frequency data of China's crude oil futures main contract from the Shanghai International Energy Exchange. The whole sample period is from March 26, 2018, to January 21, 2020, and contains 431 observations. We report the standard descriptive statistics for all variables in Table 1. Based on the statistical results, we find that all the time series of these variables are stationary. In addition, we plot the evolution of 5-min crude oil futures daily RV, jump, and negative return over the full sample in Fig. 1.

3.1. Full-sample estimation results

We report the full-sample estimation results of all prediction models in Table 2. It is evident that the values of β0 for the three prediction models are negative and significant at the 1% level, and the values of β1 for the three models are significantly positive. We find that the estimated result of βCJ is positive and significant at the 1% level, implying that the jump will lead to high fluctuation of the next day. Second, from the estimation results of the MIDAS-RV-L model, the estimated value of βL is −37.679 and significant at the 5% level, suggesting that the leverage effect also has a significant impact on Chinese crude oil futures volatility. Therefore, the in-sample results indicate that the jump and leverage effects are useful in predicting the RV of Chinese crude oil futures.

3.2. Out-of-sample prediction results

In this paper, we employ the rolling window approach to generate out-of-sample predictions, while the out-of-sample prediction length is 130. To assess the forecasting quality. we use the following two loss functions:

where m and q denote the length of the in-sample estimation period and out-of-sample evaluation period, respectively. It is well known that the MCS test of Hansen et al. (2011) is widely used in many studies of forecasting volatility (see, e.g., Wei et al., 2010; Rossi and Fantazzini, 2015; Gong and Lin, 2017). The MCS test is very useful for determining whether the forecasting model used has a statistically significant difference in out-of-sample prediction performance without specifying a benchmark model.¹We select a 25% significance level to ascertain the best model set. Namely, a prediction model will pass the MCS test if its MCS p value is larger than 0.25. Instances in which the MCS p value is greater than 0.25 are highlighted in bold. Instances in which the MCS p value is equal to 1 are highlighted in bold and underlined, implying that this prediction model exhibits the best forecasting performance. We report the MCS p values in Table 3. We find that the MIDAS-RV and MIDAS-RV-L models cannot survive in MCS because their p values are less than 0.25at one-day-ahead predictions. Obviously, only the MIDAS-RV-CJ model can pass the MCS test and yield the largest p values of 1 under the two loss functions of QLIKE and MSE, implying that the MIDAS-RV-CJ model exhibits the best predictions. These results provide evidence that a jump is very important at one-day-ahead predictions. The possible reason is that some news of international crude oil price is closely related to the volatility of Chinese crude oil futures price, and investors will make investment portfolios based on the news of international crude oil. Investors are also more sensitive when markets take big jumps. As a result, models that take into account jumps perform better when predicting volatility over the next day.

3.3. Long-term prediction results

Some market participants may focus on long-term prediction performance. However, we report the long-term prediction results in Table 4. We consider three horizons: 5-day-ahead (one week), 10-day-ahead (two weeks), and 22-day-ahead (one month). First, for 5-day-ahead predictions, we observe that the MIDAS-RV-L model yields the largest MCS p values under QLIKE and MSE; however, the MIDAS-RV and MIDAS-RV-CJ models perform poorly. Second, for 10-day-ahead predictions, we find that the MIDAS-RV model can pass the MCS test under the loss function of MSE, and the MIDAS-RV-L model still yields the largest MCS p values under QLIKE and MSE. Third, for 22-day-ahead prediction, the MIDAS-RV-L model has the best predictive power. Therefore, we can conclude that the leverage effect is more useful for long-term predictions.

4.1. Different K^max

In the previous empirical analysis, we set k^max to 22. Different k^max values may lead to completely different results. Therefore, we additionally consider two k^max values of 44 and 66. Table 5summarizes the MCS p values for different k^max. We observe that only the MIDAS-RV-CJ model can survive in MCS and yield the largest MCS p values under QLIKE and MSE, implying that the MIDAS-RV-CJ model exhibits higher prediction accuracy at a one-day-ahead horizon. In short, our results are robust to different k^max values.

4.2. Out-of-sample R²

In this subsection, we use alternative evaluation of out-of-sample R² (ROOS2), defined as:

where RVm+k, RVˆm+k and RVˆm+k,bench are the actual RV, forecast RV, and benchmark RV of Day m+k, respectively, and the definitions of m ands q are consistent with those in the loss functions QLIKE and MSE. Positive ROOS2 values indicate that this prediction model exhibits superior predictive power than the benchmark model of the MIDAS-RV model. From the results of Table 6, we find that the ROOS2 value of the MIDAS-RV-CJ model is 3.384% and significant at the 5% level, while the ROOS2value of the MIDAS-RV-CJ model is negative. In other words, our results are robust based on the out-of-sample R² test.

4.3. Alternative benchmark model

In this subsection, we employ the heterogeneous autoregressive realized volatility model of Corsi (2009) as an alternative benchmark model. Mathematically, the HAR-RV model is defined as follows:

where RVt−1, RVt−5:t−1, and RVt−22:t−1 indicate the daily, weekly, and monthly HAR components, respectively. Naturally, we can obtain the HAR-RV-CJ and HAR-RV-L models by adding jump and negative return to the HAR-RV model. Table 7shows the MCS p values when we use an alternative benchmark model of HAR-RV at one-day-ahead predictions. It can be seen that under two loss functions of QLIKE and MSE, the MIDAS-RV-CJ model has the largest MCS p values of 1. However, other competing models fail to enter the MCS with a significance level of 25%. In summary, when we consider HAR-type models, our MIDAS-RV-CJ model can still considerably improve the prediction accuracy of Chinese crude oil futures volatility at a one-day-ahead horizon (see Table 7).

4.4. Direction-of-change test

In this subsection, we further use the direction-of-change (DoC) ratio to evaluate the ability of the forecasting models to forecast the direction of change in China's oil futures volatility. We assume that pt is a dummy variable. If the predictive direction of volatility of the model is correct at Day t, then take 1; otherwise, 0:

Mathematically, the DoC rate can be computed as 1/q∑t=m+1m+qpt. Then, the nonparametric test of Pesaran and Timmermann (1992) is used to examine the null hypothesis that the DoC ratio of a target model is smaller than that of a random walk. Obviously, the direction prediction accuracy of all models is very good, exceeding 65% (see Table 8). Moreover, the MIDAS-RV-CJ model can produce the best directional prediction accuracy, reaching more than 73%.

5.1. Economic value

In this subsection, we further evaluate the economic value of each forecasting model using a mean-variance utility method introduced by Bollerslev et al. (2018). We follow the influential study of Bollerslev et al. (2018), which relies exclusively on volatility forecasts to quantify utility benefits. Mathematically, the reported utility is defined as follows:

where the definitions of m and q are consistent with those in the above loss functions. Following the work of Bollerslev et al. (2018), the annualized Sharpe ratio and coefficient of relative risk aversion are set to SR=0.4 and γ=2, respectively. The results of the averaged expected utility are shown in Table 9. We find that the MIDAS-RV-CJ model has the highest average expected utility at 3.3307, 3.3472, and 3.3453 when k^max is equal to 22, 44, and 66, respectively. This evidence also tells market participants of China's crude oil futures that more consideration of the impact of jumps can bring good economic value performance.

5.2. Expanded sample

The outbreak of the COVID-19 pandemic has severely affected the operation of the global economy, and all walks of life have been severely impacted. Financial or energy-related research during the COVID-19 pandemic has become an important hot topic (see, e.g., Ashraf, 2020; Goodell, 2020; Li et al., 2020b; Sharif et al., 2020). Therefore, we use samples that include this period for further analysis. The expanded sample period is from March 26, 2018, to April 30, 2021, and contains 751 observations. Table 10shows the in-sample estimation results using an expanded sample. We find that all parameters are significant, which is basically consistent with the conclusions in Table 2. Table 11shows the MCS p values using an expanded sample. Obviously, even if our sample period includes the period of the COVID-19 pandemic, the MIDAS-RV-CJ model is still the best model. Therefore, our results are robust to the use of an expanded sample.

5.3. Out-of-sample forecasting performance during the COVID-19 pandemic

In this subsection, we focus on investigating the prediction performance of the prediction model during the COVID-19 pandemic. Table 12reports the MCS test results during the COVID-19 pandemic. We observe that when K is equal to 22, 44, and 66, the MIDAS-RV-L model can generate the largest MCS p values of 1 under the two loss functions of QLIKE and MSE, implying that this prediction model is the best model during the COVID-19 pandemic. Why is the predictive power of the leverage effect stronger during the COVID-19 pandemic? This is an interesting question. The possible reasons are that during the period of economic prosperity or stability, a continuous bad market rarely occurs. Normal and moderate leverage is considered by investors to be normal price volatilities most of the time. Investors are more sensitive to abnormal jumps because they may contain more impact information. Second, during the COVID-19 pandemic, instability increased, the economy regressed, and the continuous bad market had a great impact on investors, causing investors to panic. At this time, the volatility jump information is second because the negative return corresponding to the leverage is more intuitive. Table 13shows the out-of-sample R² results during the COVID-19 pandemic. We observe that regardless of the value of K, the MIDAS-RV-L model can produce a significantly positive ROOS2 value. This result reaffirms that the leverage effect is the best predictor of the COVID-19 pandemic.

¹For more information about MCS, please refer to Hansen et al. (2011).

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