Chinese stock index futures experienced an unusual bull and bear markets around 2015, but its volatility dynamic is a mystery for investors and regulators. Modeling and forecasting volatility is a feasible way to reveal volatility transmission process and track market risk. In this paper, 4 HAR-type models involving jumps, realized semivariances and signed jumps are established to forecast the realized volatility of CSI 300 index futures. Based on 4 basic HAR-type models, HARQ-type models and HARQF-type models are proposed by adding correction term of median realized quarticity (MedRQ). During the modeling process, two decompositions of realized volatility including continuous and jump variances, upside and downside realized semivariances are considered. To reduce the robustness of market microstructure noise, the optimal sampling frequency for calculating realized volatilities is determined by the minimum MSE criterion, the statistic Zmed of ADS jump test, realized semivariances and signed jump are revised based on realized kernel estimator. The newly MCS test is employed to evaluate the out-of-sample forecast performances. In-sample and out-of-sample analysis of forecast models are carried out on CSI 300 index futures, which shows important conclusions:1)Most of the predictable variation in realized volatility stems from continuous volatility rather than jump variance, and future realized volatility is more related to historical downside semivariances (bad volatility) than upside semivariances (good volatility); 2) Good volatility and bad volatility exhibit asymmetric impact effect that good (bad) volatility generate negative (positive) impact on future realized volatility; 3)Decomposition of upside and downside realized semivariances outperforms that of continuous and jump variances; 4) MedRQ can significantly enhance the forecast ability of HAR-type models, HARQF models outperform HARQ models on in-sample performances, while HARQ models achieve better out-of-sample forecast accuracy; 5) Signed jumps bear valuable information of both market volatility and directions, and HARQ-RV-SJ is the best model among all forecast models specified in our paper. Our findings have import implications for investors and policymakers to grasp the volatility and risk of Chinese stock index futures.
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