Time-varying jump intensity and volatility forecasting of crude oil returns

Modelling and forecasting of crude oil volatility have been widely examined using GARCH-type models, and evidence suggests the presence of time-varying jumps in the crude oil market. This paper proposes a novel approach to model and forecast crude oil volatility by incorporating two time-varying jump intensities (State-dependent and Hawkes process) into the GARCH-Jump model. Our in-sample and out-of-sample analysis demonstrates that considering jump intensity as an explanatory variable significantly enhances the forecasting accuracy of WTI and Brent crude oil volatility. For WTI crude oil volatility, the more complex the jump intensity model, the better its forecasting power. For Brent crude oil volatility, the picture is different, indicating that the non-linear characteristics of volatility provide more informative forecasts. Further analysis shows that, during the COVID-19 crisis period, the Hawkes Jump Intensity (HJI)-GARCH model consistently improves the volatility forecasting performance. These results highlight the importance of jump intensity in modelling and predicting crude oil price volatility.