A hybrid learning approach integrating ARIMA-GARCH-LSTM for value-at-risk forecasting

Accurate Value-at-Risk (VaR) forecasting provides a methodical approach for quantifying possible financial losses. This study introduces a hybrid forecasting model that integrates deep learning-specifically Long Short-Term Memory (LSTM) networks- with conventional ARIMA-GARCH models to enhance VaR forecast accuracy. The model forecasts the returns of WTI crude oil for 954 days by integrating both linear and nonlinear structures while accounting for conditional volatility. Using parametric and historical simulation methods, it also estimates VaR at 99%, 95%, and 90% confidence levels. Hybrid forecasts of VaR are obtained by combining predictions from both models. The estimated VaR performance for hybrid models is evaluated using WTI crude oil returns through conditional and unconditional coverage tests and regulatory and firm-specific loss functions. This period includes both the extreme volatility of the COVID-19 pandemic and more stable market conditions. The findings indicate significant improvements in VaR prediction precision for the proposed hybrid model compared to the benchmark models. GARCH models perform relatively well in the historical simulation method at the 95% confidence level. However, this method tends to underestimate risk during periods of extreme volatility, while the parametric method demonstrates much stronger performance across all confidence levels. Overall, deep learning-based hybrid models outperform traditional models in the parametric framework, with the ARIMA-eGARCH-LSTM model achieving the lowest loss rates across all tests and providing VaR estimates closest to the realized losses.