Before revision: A new realized joint Value-at-Risk (VaR) and expected shortfall (ES) regression framework is proposed, through incorporating a measurement equation into the original joint VaR and ES regression model .
After revision: A new realized joint Value-at-Risk (VaR) and expected shortfall (ES) regression framework is proposed, through incorporating a measurement equation into the original quantile regression model. The framework is further extended by employing various Expected Shortfall (ES) components, to jointly estimate and forecast VaR and ES regression model .