Backtesting Expected Shortfall for Bitcoin: A Joint Combined LSTM-Based Approach

This work aims to identify the most accurate model in passing the joint-combined backtesting procedure for Value-at-Risk and Expected Shortfall forecasts for Bitcoin. First, GARCH and Markov Switching GARCH are estimated and used to forecast the corresponding VaR and ES. Next, the Long Short-Term Memory model is applied to refine these risk measures. Finally, four models (GARCH, Markov-Switching GARCH, Joint-Combined, Long-Short Term Memory Joint-Combined) are compared based on average loss and backtesting performances. Results suggest that the LSTM-Joint-Combined model apparently represents the best model delivering the lowest average predictive loss across the evaluated settings. Furthermore, it considerably enhances the efficacy of the J-C approach.