Do realized higher moments have information content? - VaR forecasting based on the realized GARCH-RSRK model

In this paper, we develop a new model, the Realized GARCH-RSRK, to determine the time-varying distribution of financial returns with realized higher moments. Based on Gram-Charlier expansion (GCE) density, we first explicitly link the expansion parameters with moments that are calculated based on intraday returns using our new model. Then, the Cornish-Fisher expansion is applied to forecast Value-at-Risk (VaR) with estimated moments to demonstrate the economic significance of this new model. Compared with the daily-return-based dynamic higher moments models, the inclusion of realized higher moments significantly improves this model's ability to forecast extreme tails. The empirical results indicate that this new model outperforms the benchmark models when forecasting extreme VaR. In addition, we provide a formula to correct the moments associated with the commonly used squared transformation of GCE. Our empirical evidence highlights the importance of using corrected moments in VaR forecasting. • We propose a new model, the Realized GARCH-RSRK, to model realized higher moments. • Our model outperforms the benchmarks in terms of the extreme VaR forecasting. • The realized higher moments are crucial for modeling extreme tail dynamics. • We find a significant distortion between correct moments and GCE moment parameters. • The corrected formulas for moments we derived are supported by empirical evidence.