A coupled realised real-time EGARCH model with filtered historical simulation

Abstract This paper introduces a Coupled realised real-time EGARCH model with Filtered Historical Simulation (FHS), referred to as the “CouRTES” model, as an extension of the Realised EGARCH-type models for multi-horizon volatility and distributional forecasting. The model decomposes daily log-returns into overnight and intraday components and jointly models their conditional variances through a coupled bivariate log-variance system, while preserving the interpretable aggregation $$h_t=h_t^{O}+h_t^{I}$$ . The volatility recursion incorporates a realised measure channel, constructed from overnight variation and intraday realised variance, and a same-day real-time proxy observable by the market close. The FHS layer resamples filtered innovations to generate predictive distributions without imposing a restrictive parametric innovation law. Empirically, the CouRTES model is evaluated using daily S&P 500 data with 5-minute realised variance over the effective sample from 2000 to 2020. The results show that CouRTES delivers strong realised measure forecasting performance within the GARCH family comparison. Under QLIKE loss, CouRTES records the lowest loss in 11 out of 14 horizons and has lower mean QLIKE loss in 36 out of 42 Diebold-Mariano comparisons against GARCH family benchmarks, with 22 comparisons significant at the 5% level. The Model Confidence Set analysis further supports the statistical credibility of CouRTES, retaining the model in 13 out of 14 horizons under QLIKE loss. CouRTES also improves over the EWMA benchmark across all reported QLIKE horizons, but remain competitive to HAR-RV model only on realised volatility point forecasting. In addition to point-forecast accuracy, the FHS layer of the CouRTES model produces empirically plausible predictive intervals, with average coverage of approximately 0.878, close to the nominal 90% level. Overall, the results support CouRTES as a statistically credible and operationally feasible Realised EGARCH-type models extension for coupled overnight-intraday volatility modelling, real-time updating, and distributional risk forecasting.