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Title: Functional GARCH-X Model with an application to forecasting crude oil return curves Authors:  Yuqian Zhao - University of Essex (United Kingdom) [presenting]
Gregory Rice - University of Waterloo (Canada)
Tony Wirjanto - University of Waterloo (Canada)
Abstract: Functional data objects derived from high-frequency financial data are uncorrelated but long-range conditionally heteroscedastic. The existing functional GARCH models are designed to account for conditional heteroscedasticity, but not specifically to capture long-range dependent dynamics in the data. We propose a functional GARCH-$X$ model, where the covariate $X$ is chosen to be weakly stationary with a long-range dependence property. The functional autocorrelation coefficients of the squared process of this and other recently introduced functional volatility processes are studied. Monte Carlo simulation shows that the functional autocorrelation coefficients of the squared functional GARCH-$X$ process behave closely to those observed in the empirical data. In an empirical application, we forecast conditional volatility of the WTI crude oil intra-day return curves collected from the commodity futures market. The results show that the FGARCH-$X$ model provides mild corrections to the functional volatility models in terms of the conditional volatility prediction, yielding more precise confidence bands for the return curves.