Exploring volatility of crude oil intraday return curves: a functional GARCH-X model

Crude oil intraday return curves collected from commodity futures markets often appear to be serially uncorrelated and long-range conditionally heteroscedastic. We model this stylised feature with a newly proposed functional GARCH-X model and use it to forecast crude oil intraday volatility. The predicted intraday volatility provides important economic implications in crude oil commodity futures markets in both intraday risk management and utility benefits improvements. The functional GARCH-X model provides a remarkable correction to modelling crude oil volatility in terms of an in-sample fitting, although its out-of-sample performances in forecasting intraday risk measures do not appear to be significantly superior to that of the existing functional GARCH(1,1) model. However, the FGARCH-X model, with its flexibility to capture long-range dependence and potential seasonality, does confer substantial economic benefits by embedding inter-daily volatility forecasts. Methodologically, we show that the new model has a well-behaved stationary solution, and we also address the inherent and critical issues associated with the estimation of functional volatility models by introducing novel data-driven, non-negative and predictive basis functions in the estimation process.