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Long-range functional volatility models with an application to forecasting crude oil return curves
Abstract: Functional data objects derived from high-frequency financial data often exhibit volatility clustering. Versions of functional generalised autoregressive conditionally heteroscedastic (FGARCH) models have recently been proposed to describe such data. We found intra-day asset return curves are long-range conditional heteroscedastic, however, the existing functional ARCH and GARCH models are not specifically designed to capture this type of dynamics. In this paper, we aim at modelling long-range dependence in the conditional volatility of asset returns. Two variants of the FGARCH model are introduced: a functional ARCH ($\infty$) representation and a FGARCH-X model, where the covariate $X$ is designed to be long-range dependent through information collected at a longer time horizon. In addition, basic diagnostic tests for FGARCH-typed models are still not available so far, we propose two portmanteau type tests to evaluate adequacy and inform order selection of these models. Simulation results show that both tests have good size and power to detect model mis-specification in finite samples. Empirically, we model and forecast the volatility of the WTI crude oil intra-day return curves collected from the commodity future market. The results show that, although both of the FGARCH and FGARCH-X models are adequate to explain the conditional heteroscedasticity, latter are preferred when they are used to forecast intra-day volatilities, allowing us to provide valid and more conservative intra-day Value-at-Risk for the return curves.
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