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.