Abstract: The accurate forecasting of volatility in the crude oil futures market is an important issue, which has attracted considerable attention from academics, investors, businessmen and governments. This paper mainly aims to test whether the crude oil futures market has obvious jump risk and structural breaks, and investigate whether these two factors can be used to predict the volatility of crude oil futures. Considering jump risk and structural breaks, the HAR-RV-J-SB, HAR-S-RV-J-SB, and PSlev-J-SB models are developed on the basis of HAR-RV, HAR-S-RV, and PSlev models. Then, applying the transaction data of 5-min WTI crude oil futures from the NYMEX-CME, the in-sample and out-of-sample performances of the above models are analyzed. The empirical results show that the crude oil futures market has obvious jump risk and structural breaks. The out-of-sample performances of the HAR-RV-J-SB, HAR-S-RV-J-SB, and PSlev-J-SB models are better than those of the corresponding HAR-RV, HAR-S-RV, and PSlev models, and the results are robust. In particular, similar results can be obtained when jump risk and structural breaks are added to other existing HAR models such as the HAR-C and LHAR-RV models. The above results suggest that considering jump risk and structural breaks can significantly improve the performances of most existing HAR-type models for predicting the volatility of crude oil futures, so these two factors cannot be ignored when proposing new HAR-type models for modeling and forecasting the volatility of crude oil futures. Additionally, the HAR-type models with jump risk and structural breaks developed in this paper perform good predictive powers for the volatility of crude oil futures. The results contribute to the decision of financial traders for portfolio allocation and risk management plan, the industrial production of manufacturers, as well as the relevant policy setting of policymakers.

Key words: jump risk, structural breaks, volatility forecasting, HAR-type models, MCS test