E-Backtesting Expected Shortfall without Value-at-Risk Forecasts under Time-series Models
无需VaR预测的期望损失E-回测:时间序列模型下的方法
Expected Shortfall (ES) measures the average size of tail losses. Its sequential backtests typically also require a Value-at-Risk (VaR) forecast. We develop two e-backtesting methods using only observed losses and ES forecasts: one for iid losses only and the other for time series under an AR-GARCH conditional VaR structure. Under the stated assumptions, both control false rejections at any stopping time. For the time-series method, validity requires a fixed…