S1 Appendix -

<div><p>The realized recurrent conditional heteroscedasticity (RealRECH) model improves volatility prediction by integrating long short-term memory (LSTM), a recurrent neural network unit, into the realized generalized autoregressive conditional heteroskedasticity (RealGARCH) model. However, at present, there is no literature on the ability of the RealRECH model to fit and predict volatility in the Chinese market. In this paper, a study is conducted to test the in-sample explainability and out-of-sample prediction ability of the RealRECH model for the SSE50, CSI300, CSI500 and CSI1000 indices in the Chinese market and to determine whether it performs better than the RealGARCH model. The results of the in-sample analysis show that the RealRECH model not only provides better in-sample interpretability for all four indices but also captures the complex dynamics of time series volatility that the RealGARCH model cannot capture, such as long-term dependence and nonlinearity. The results of out-of-sample volatility prediction show that the RealRECH model better predicts the volatility of the CSI500 and CSI1000 indices but yields worse predictions for the SSE50 and CSI300 indices. Thus, the RealRECH model can be used for CSI500 and CSI1000 prediction.</p></div>