Deep Quantile Forecasting: Evaluating Advanced Neural Networks for Multi-Horizon Value-at-Risk

This study examines whether modern deep learning architectures can improve multi-horizon value-at-risk (VaR) forecasting by learning nonlinear tail-risk dynamics that are difficult to capture with conventional econometric models. Using S&P 500 return data and realized volatility measures, we compare quantile regression (QR), Light Gradient Boosting Machine (LGBM), and five neural architectures—MLP, LSTM, TCN, TiDE, and TFT—within HAR, CAViaR, and realized-volatility-augmented CAViaR specifications across 1% and 5% VaR at 1-day, 5-day, 10-day, and 22-day horizons. Forecast performance is evaluated using pinball loss, formal VaR backtests, and the model confidence set procedure. The results suggest that the performance of deep neural architectures depends on the forecast horizon and the structure of the underlying tail-risk dynamics. In particular, gated memory, attention-based learning, and multi-horizon sequence design appear to improve conditional quantile forecasting by better capturing persistence, nonlinear dependence, and regime-sensitive behavior. At the same time, stronger statistical forecasting accuracy does not automatically imply regulatory validity, since a VaR model must also satisfy formal coverage and independence tests. Overall, the findings highlight the distinction between predictive skill and regulatory adequacy in financial risk measurement.