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This article seeks to examine the forecasting performance of competing models for intra-day volatility for the IBEX-35 index futures market. Whilst the use of intra-day is becoming common in examining daily forecasts through realized volatility, relatively little research examines the forecasting performance of models designed to capture intra-day volatility itself. The results presented here suggest first that the Hyperbolic Generalized Autoregressive Conditional Heteroscedasticity (HYGARCH) model provides the best forecast of intra-day volatility. Second, both this model and the Fractionally Integrated Exponential GARCH (FIEGARCH) model are particularly good at very high-frequency forecasts (less than 1 hour). Third, the Integrated-GARCH and FIGARCH models perform better at frequencies of 1 hour and lower. Fourth, the Component-GARCH model appears to provide a consistent performance across several frequencies. Fifth, the FIEGARCH model performs particularly well when weighting underpredictions of volatility higher than overpredictions. Overall, the results presented here are of interest to both academics, those engaged in microstructure modelling and practitioners interested in volatility and interval forecasting and dynamic hedging.
