key: cord-0993832-q09jkkyj authors: Lu, Xinjie; Ma, Feng; Wang, Jiqian; Wang, Jianqiong title: Examining the predictive information of CBOE OVX on China’s oil futures volatility: Evidence from MS-MIDAS models date: 2020-09-01 journal: Energy (Oxf) DOI: 10.1016/j.energy.2020.118743 sha: d0ca63f85123eed81c7103e9712918262a7603cc doc_id: 993832 cord_uid: q09jkkyj This study evaluates whether CBOE crude oil volatility index (OVX) owns forecasting ability for China’s oil futures volatility using Markov-regime mixed data sampling (MS-MIDAS) models. In-sample empirical result shows that, OVX can significantly lead to high future short-term, middle-term and long-term volatilities with regard to Chinese oil futures market. Moreover, our proposed model, the Markov-regime MIDAS with including the OVX (MS-MIDAS-RV-OVX), significantly outperforms the MIDAS and other competing models. Unsurprising results further confirm that OVX indeed contain predictive information for oil realized volatility (especially significant and robust in middle-term and long-term horizons) and regime switching is useful to deal with the structural break within the energy market. We carry out economic value analysis and discuss OVX’s asymmetric effects concerning different trading hours and good (bad) OVX, and find OVX performs better in day-time trading hours and the good OVX is more predictive for the oil futures RV than the bad OVX. The further discussion also confirms our previous conclusions are robust during the highly volatile period of the COVID-19 pandemic. Always known as the king of commodity by industry insiders, crude oil is directly or indirectly used in all industries because of its extensive participation in our everyday life. Thus, fluctuations of crude oil play an important role in the development of the commodity and even the national economy, which attracts plenty of researchers to carry out related explorations (Kilian and Park, 2009; Ma et al., 2018; Mo et al., 2019; Sek, 2019; Wang et al., 2019a; Gong et al., 2020) . For instance, Gong et al. (2020) demonstrated that higher oil price has brought negative effects to the global economy. Proposed by the Chicago Board of Options Exchange (CBOE), OVX is an immediate measurement of investors' uncertainty of future crude oil prices changes, which makes OVX an interesting uncertainty index for investors, policy makers and scholars. OVX is popularly applied in the volatility forecasting of different markets, for instance, clean energy equity markets (Dutta, 2017; Ahmad et al., 2018) , China's stock markets ( Luo and Qin, 2017; Xiao et al., 2018; Xiao et al., 2019) , China's commodity markets (Jin and Zhu, 2019), metal markets (Dutta, 2018; Dutta et al., 2019) , Bitcoin prices (Al-Yahyaee et al., 2019; Das et al., 2019) . From the stands of literature, with regards to the oil markets, some studies (Aboura and Chevallier, 2013; Liu et al., 2013; Haugom et al., 2014; Chen et al., 2018; Lv, 2018) have also investigated the predictive ability of CBOE OVX on forecasting international oil markets volatility (e.g., WTI and Brent). For instance, Lv (2018) evaluates whether OVX is helpful for forecasting the WTI futures volatility based on the HAR-RV models. They find that OVX indeed positively affects oil futures RV and the larger OVX has more powerful performance than smaller ones. 1 https://www.chinadaily.com.cn/a/201903/27/WS5c9b088fa3104842260b2db4.html. 2 https://www.wsj.com/articles/chinas-oil-futures-give-new-york-and-london-a-run-for-their-money-11553679002. J o u r n a l P r e -p r o o f Haugom et al. (2014) examine whether OVX is capable of forecasting RV in the WTI futures market, and verify that adding OVX to the HAR-RV model makes the model better fits RV time series. Ji and Fan (2016) examine the interdependence such as direction, dynamics, magnitude and asymmetry relationship between WTI and OVX by applying a time-varying parameter (TVP) GARCH model. They find that the interdependence between the OVX changes and WTI returns is significantly negative, and the time-varying results show that it is not always negative. Chen et al. (2018) utilize GARCH-type models to prove that CBOE OVX owns predictive ability for WTI and Brent market. They verify that adding OVX to the GARCH-type model improves forecasting accuracy even in longer predictive periods of 5 and 20 days. With regards to the China's crude oil futures market, researches on this market are rare. As far as we know, till now, there are nearly five literature about this newly emerging crude oil futures (Ji and Zhang, 2019; Chen et al., 2019; Wang et al., 2019b; Li et al., 2020; Yang and Zhou, 2020) . More specifically, Ji and Zhang (2019) price returns based on the multifractal characteristics, and they find the multifractality degree of China's crude oil futures is greater than WTI but weaker than Brent. Yang and Zhou (2020) investigate the return and volatility transmission between China's crude oil futures and international crude oil futures markets. Li et al. (2020) examine the relationships between Chinese crude oil futures and its two underlying crude oil spots from the perspective of hedging. However, the research on China's crude oil's volatility is J o u r n a l P r e -p r o o f extremely rare and we tryto investigate the relationship between OVX and China's oil futures volatility in this paper. Hailing from the existing literature, two obvious features need to be extremely emphasized here, which really motivate us to carry out this research. The first is that most literature focus on the volatility of international oil markets such as WTI and Brent, and research on China's oil futures market is extremely rare. Second, the existing researches mainly focus on HAR-RV or GARCH-type models and few literatures apply MIDAS models to predict oil RV. However, we pick MIDAS models to predict oil futures RV for following reasons. First, MIDAS-RV model is capable of better reflecting heterogeneity than the HAR-RV model because HAR-RV model is a special evolution from the MIDAS-RV model (Ghysels et al. 2006 (Ghysels et al. , 2007 (Ghysels et al. , 2009 ). In addition, MIDAS-RV model is popularly applied and practical applications further confirm that MIDAS models obtain more powerful forecasting performances than other models (Alper et al., 2012; Santos and Ziegelmann, 2014; Ma et al., 2019) . For instance, Santos and Ziegelmann (2014) find MIDAS prediction is superior to several multi-period volatility forecasting models such as HAR, MIDAS and their combination methods. Ma et al. (2019) find the MIDAS-RV may better reflect heterogeneity than the HAR-RV model. As far as we know, only two literature predict intraday oil futures volatility relying on MIDAS framework (Degiannakis and Filis, 2018; Mei et al., 2020) . Furthermore, the result of structural breaks test show structural breaks indeed exist in China's oil futures markets, which makes regime switching reasonable to be considered in our model. In addition, Kuck and Schweikert (2017) and Uddin et al. (2018) demonstrate that regime switching is more efficient to forecast the oil market volatility. Therefore, this J o u r n a l P r e -p r o o f paper purposely investigates the predictability of OVX on China's oil futures volatility using novel Markov-regime mixed data sampling (MS-MIDAS) models. In order to seek for the potent relationship between OVX on China's oil futures volatility, we carry out the empirical analysis as follows. First, we pick MIDAS-RV and its extended models to predict Chinese oil futures RV. The rolling window method is applied and out-of-sample forecasting performances are assessed by Model Confidence Set test (MCS). Second, we investigate the economic value of our proposed models. stands out in the model set, implying that considering the combination of OVX information and regime switching together can achieve more satisfying predictive performance, especially significant and robust in medium-term and long-term horizons. Moreover, we find the economic gains of MS-MIDAS-RV-OVX model are the largest among our proposed models. Furthermore, we also find OVX performs better in day-time trading hours and the good OVX is more predictive for the oil futures RV than the bad OVX. During the COVID-19 pandemic, similar findings are also obtained. What's more, these results are especially significant and robust in horizons of medium-term and long-term. The remainder of our article is presented as follows. Next part makes a brief presentation of the realized measurement, benchmark and the related predictive models. Section 3 shows descriptive statistics such as the mean, standard error, skewness and kurtosis of variables. Section 4 shows the predictive results from in-sample, out-of-sample prediction, economic value and robustness checks. Section 5 presents the J o u r n a l P r e -p r o o f discussion about OVX's asymmetric effects. Section 6 presents discussion about COVID-19 pandemic. Section 7 concludes the paper. Produced by Andersen and Bollerslev (1998) , RV holds the advantages of non-parametric and easier computation (Meddahi et al., 2011) . Following Meddahi et al. (2011), for a certain trading day t, the squared intraday high-frequency returns can be constructed as: where , represents the intraday return of day t, presents the amounts of observations. According to Barndorff-Nielsen and Shepherd (2004) , RV can be presented as follows, when Δ → 0: where ( ) is the integrated variance (IV) which can be calculated by realized bi-power variation (BPV) as follows: where $ = )2/+ ≈ 0.7979. ∑ ( ) ! presents the jump components. J o u r n a l P r e -p r o o f We apply MIDAS-type models to predict RV of oil futures, and our benchmark model from Ghysels et al. (2007) can be expressed as follows 3 . RV , 1 = 2 + 2 ∑ 3( , 4 56 , 4 56 )RV %7 + 8 1 where < , 1 = 1 ℎ( < , 1 + < 1 , 1 … + < 1 % , 1 ) ⁄ , and < %7 denotes lags (t-k) of RV. For instance, < % represents the lag one of RV. In this paper, is equal to 50. We choose this model as the benchmark and do further evaluations on its forecasting ability on oil futures volatility with the extended models. We mainly try to evaluate whether CBOE OVX owns valuable predictive information for China's oil futures volatility based on MIDAS models in our study. As abovementioned, few studies focus on the relationship between OVX and China's oil futures volatility from a quantitative aspect. Therefore, we naturally add OVX as an additional variable to the basic MIDAS model and construct following model, which is 3 The code is available upon request. RV , 1 = 2 ,R S + 2 ,R ∑ 3( , 4 56 , 4 56 )RV %7 + 8 S where To have a closer look at whether OVX can have different performances during high or low volatility period, we naturally built MS-MIDAS-RV-OVX (Model 4). RV , 1 = 2 ,R S + 2 ,R ∑ 3( , 4 56 , 4 56 )RV %7 Information for the typology of the four models discussed in this paper is summarized in Table 1 . Insert Proposed by Chicago Board Options Exchange (CBOE), OVX is a measurement for market's expectation for future 30-day crude oil price volatility 4 . The OVX data is from the CBOE website (http://www.cboe.com/). We finally gain 423 trading days for the whole sample period. The descriptive statistics of variables are summarized in Table 2 . From Table 2 , we observe that all the data series skew rightly and hold the characteristics of high kurtosis. From the Jarque-Bera (JB) statistic test, we find there is no hint of Gaussian distributions within the data series at the 1% significance level. The evidence that oil RV and OVX data series own serial auto-correlations up to the 22th order is gained from the Ljung-Box test. Finally, Augmented Dickey-Fuller (ADF) test proved that at the 1% significance level, there is no hint of unit root, which gives an evident sign that all the data series are stationary in levels. Insert Table 2 to construct daily, weekly and monthly OVX , which can be presented as OVXd, OVXw and OVXm respectively. It is of vital importance that in-sample forecasting is capable of predicting, and the predictive information of benchmark and extended models is contained in Table 3 . Several findings indeed draw our attentions. Firstly, the coefficient parameters for RV within all the models are all significant at the 1% significance level, reflecting the past oil realized volatility can cause a higher volatility in the future. Besides, the parameter estimates of OVX in the MIDAS-RV-OVX model is remarkably positive at the 10% significance level in the midium-term horizon (h = 5) and remarkably positive at the 5% significance level in the long-term horizon (h = 20), indicating that OVX can predict oil market volatility especially in medium-and long-term horizons. There is no doubt that out-of-sample predictive ability is of vital significance for volatility forecasting, owing to it is capable of reflecting the model's future prediction performance which the market participants really focus on. To avoid the overlapping of data, we apply rolling window approach to do the prediction and make out-of-sample prediction maintain an unchangeable length (in our paper, it is 300 observations.). There is no doubt that out-of-sample predictive ability is of vital importance in volatility forecasting, because of its capacity to reflect the model's future prediction performance. To keep step with Patton (2011), As a result, the QLIKE and MSE loss functions were applied to carry out out-of-sample evaluation. These two loss functions are defined as follows: where RV h m indicates the out-of-sample forecasting realized volatility from the forecasting model, while RV is the actual volatility during the same period. L represents the length of evaluation period. To further confirm the models' predictive performance, we combine Model 5 These numbers can be obtained from http://www.ine.cn/news/area/2801.html. (12) and (13) Moreover, stationary bootstrap 6 method is picked to evaluate the interpretation of the MCS test p-value. The proposed models' predictive ability from MCS test is exhibited in It is undeniable that out-of-sample predictive performance is of vital significance for volatility forecasting. However, as "Economic Man", it cannot be neglected that market investors keep their eye closely on the economic value of the proposed model. In this part, following Guidolin and Na (2006) where s * is the optimal weight of Chinese oil futures, p is the excess return ( p = − ,u ), is the oil futures return, and ,u is risk-free rate (here we apply the three-month Shanghai Interbank Offered Rate (SHIBOR) 7 ) and M is a risk aversion coefficient. s * p + ,u can be used to define portfolio return. On the (t+1) th day, the ex-ante optimal weight of Chinese oil futures can be calculated by the function below: can be written as, where $ " … and RV m " refer to mean and variance of portfolio returns, respectively. The results of economic value analysis are reported in Table 5 China's oil futures, and its predictive performance is more significant and robust during medium-term and long-term periods. In other words, the results from economic value analysis are consistent with out-of-sample results. Insert To further identify whether our above-mentioned results are robust or not, this section presents the application of realized kernel (RK), another commonly used variance J o u r n a l P r e -p r o o f estimator of Barndorff-Nielsen et al. (2008) , and it can be expressed as follows: where k(x) is the Parzen kernel function, and H is a bandwidth parameter (Barndorff-Nielsen et al., 2009) . Several findings are presented here. From 8 We further examined other lag lengths and the results are very similar. where RV is the actual realized range-based volatility, RV is the estimation from model , and ∈ Model (0,1, 2, 3) . < is the volatility forecasting from the benchmark model. When ˆˆ is positive, this means the related model have an excellent predictive performance over the benchmark model. Following Clark and West (2007) Results are presented in Table 9 . Insert Table 9 Insert Patton and Sheppard (2015) firstly propose the method of decomposing RV into good and bad volatility and evaluate whether downside and upside risk can trigger different effects by using realized semi-variance estimators (Barndorff-Nielsen et al., 2009 ). This method is popularly applied in volatility forecasting and modeling (Baruník et al., 2016; Bollerslev et al., 2018; Kilic et al., 2019) . Inspired by them, we classify OVX into good and bad OVX and evaluate whether they have asymmetric performances and they can be presented as: where " () is the indicator function, and is the return of Chinese oil futures. OVX -1 (OVX -% ) can be calculated as the sum of all available positive (negative) OVX. In this part, we apply out-of-sample test to assess the models' predictive accounted for more than 80% of global oil demand growth. 9 Thus, it is such an interesting issue for us to detect whether OVX contain predictive information for China's oil futures market during the COVID-19 pandemic. In this section, the predictive sample period ranges from December 08, 2019 to April 16, 2020 10 . And we finally get 77 observations for the COVID-19 pandemic discussion. The results are presented in Table 14 . It is unsurprising that the MS-MIDAS-RV-OVX model still stands out in the best model set, which can be observed from the evidence that (1987), we set the null hypothesis of normal distribution for each variable. Ljung and Box (1978) propose the Ljung-Box statistic called Q(n), in our study, we test the 5 th and 22 th order serial correlation. Asterisk *** , ** and * denote rejections of null hypothesis at 1%, 5% and 10% level. In this table, p value less than 0.1 are meaningful. Notes: This table reports the CER for a mean-variance function, which reflects an investor's assets assignments between oil futures and a risk-free asset. Out-of-sample results. Forecasting models h=1 h=5 h=20 Leverage vs. feedback: Which Effect drives the oil market? Optimal hedge ratios for clean energy equities MIDAS volatility forecast performance under market stress: Evidence from emerging stock markets Can uncertainty indices predict Bitcoin prices? 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A comparison with gold, commodity and the US Dollar Forecasting oil prices: High-frequency financial data are indeed useful Oil price uncertainty and clean energy stock returns: New evidence from crude oil volatility index Impacts of oil volatility shocks on metal markets: A research note Nonlinear relationships amongst the implied volatilities of crude oil and precious metals Geopolitical risk uncertainty and oil future volatility: Evidence from MIDAS models Does US Economic Policy Uncertainty matter for European stock markets volatility Visiting effects of crude oil price on economic growth in BRICS countries: Fresh evidence from wavelet-based quantile-on-quantile tests Forecasting the equity risk premium: the role of technical indicators Volatility forecast comparison using imperfect volatility proxies Good volatility, bad volatility: Signed jumps and the persistence of volatility Déjà vol': Predictive regressions for aggregate stock market volatility using macroeconomic variables Déjà vol': Predictive regressions for aggregate stock market volatility using macroeconomic variables Volatility forecasting via MIDAS, HAR and their combination: An empirical comparative study for IBOVESPA Unveiling the factors of oil versus non-oil sources in affecting the global This table shows out-of-sample performance of models' evaluation by This study investigates which predictors (VIX or EPU index) are useful to forecast future volatility during coronavirus pandemic The authors are grateful to the editor and anonymous referees for insightful comments that significantly improved the paper. This work is supported by the Natural Science The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.