Forecasting Value-at-Risk and Expected Shortfall using penalized quantile regressions with mixed-frequency data

Value-at-Risk (VaR) and Expected Shortfall (ES), as two essential tools for risk management, have received widespread attention for their ability to provide financial institutions with a quantitative measure of potential losses. This paper considers a mixed-frequency quantile regression model to enhance the accuracy of VaR and ES predictions. We propose a multi-step estimation procedure based on penalized quantile regression methods and establish a goodness-of-fit test using a bootstrap approach. Simulation studies demonstrate that the Elastic Net penalized quantile regression performs well in identifying significant lags in time series data with high correlations, and our proposed bootstrap testing approach performs effectively. Empirical results from three representative Asian stock markets indicate that our methods achieve high accuracy in VaR and ES predictions.