Nonparametric expected shortfall forecasting incorporating weighted quantiles

A new semi-parametric expected shortfall (ES) estimation and forecasting framework is proposed. The proposed approach based on a two-step procedure. first step involves the of value at risk (VaR) different quantile levels through set time series regressions. Then, ES computed as weighted average estimated quantiles. weighting structure parsimoniously parameterized by means beta weight function whose coefficients are optimized minimizing joint VaR loss Fissler–Ziegel class. properties evaluated with an extensive simulation study using two data generating processes. Two studies out-of-sample sizes then conducted, one which focuses 2008 Global Financial Crisis period. models applied to seven stock market indices, their performances compared those range parametric, non-parametric, models, including GARCH, conditional autoregressive expectile (CARE), regression simple results experiments provide clear evidence in support models.