Loss‑based Bayesian Sequential Prediction of Value at Risk with a Long‑Memory and Non‑linear Realized Volatility Model
The RNN-HAR model, integrating Recurrent Neural Networks with the heterogeneous autoregressive (HAR) model, is proposed for Value at Risk (VaR) forecasting. It effectively captures long memory and non-linear dynamics. Empirical analysis from 2000 to 2022 shows RNN-HAR outperforms traditional HAR models in one-step-ahead VaR forecasting across 31 market indices.