We investigate the effect of estimation error on backtests of (multi-period) expected shortfall (ES) forecasts. These backtests are based on first order conditions of a recently introduced family of jointly consistent loss functions for Value-at-Risk (VaR) and ES. We provide explicit expressions...

Tail expectations have recently attracted much attention in economics for their ability to capture risk. We develop a semiparametric estimator for the joint estimation of (nonlinear) models of tail expectations with some tail quantile as left or right threshold, and interquantile expectations,...