An outlier-robust dynamic semiparametric model for jointly forecasting value-at-risk and expected shortfall

<title>Abstract</title> <p>A joint dynamic semiparametric framework based on Fissler--Ziegel (FZ) loss minimization has recently received increasing attention for forecasting value-at-risk (VaR) and expected shortfall (ES). However, existing models typically do not account for the outliers, though such observations frequently occur in financial time series and may distort risk forecasts. To address this issue, this paper proposes an outlier-robust joint dynamic semiparametric model by incorporating bounded innovation propagation (BIP) into the conditional autoregressive value-at-risk (CAViaR) framework. By limiting the effect of extreme observations on the updating process, the proposed BIP-CAViaR-FZ model delivers more robust forecasts of both VaR and ES while maintaining semiparametric flexibility. The standard CAViaR-FZ model is nested as a special case. Simulation results show that the proposed model enhances the accuracy of VaR and ES estimation and forecasting in the presence of outliers, with this advantage being particularly pronounced under the skewed heavy-tailed distribution and at lower probability level. Furthermore, empirical findings demonstrate that the proposed model outperforms the standard non-robust competing counterpart in terms of both VaR and ES forecasts, thereby corroborating its robustness and effectiveness for joint VaR and ES prediction in practical applications.</p>