Conditional expectile-based value-at-risk: Semiparametric estimation and inference

Conditional expectile-based value-at-risk (EVaR) has attracted increasing attention in financial risk management owing to its desirable theoretical properties. However, existing estimation methods for conditional EVaR either rely on potentially misspecified parametric models or suffer from the curse of dimensionality in nonparametric approaches. To this end, we study semiparametric estimation and inference for conditional EVaR in nonlinear time series models with unspecified error distribution. Specifically, we propose a two-step conditional EVaR estimator that achieves the parametric convergence rate. Furthermore, we derive a functional central limit theorem for conditional EVaR process, and then extend to investigate estimating both conditional expectile-based expected shortfall and conditional distribution. A residual bootstrap procedure is proposed for non-expert practitioners to conduct statistical inference. The asymptotic results and their applications are illustrated by numerical studies and an empirical application to S\&P 500 returns.