Forecasting value-at-risk and expected shortfall using fractionally integrated models of conditional volatility: International evidence

► VaR and ES forecasting for fractionally integrated ARCH models for 20 stock indices. ► Long memory in conditional variance does not improve the multi-period VaR and ES. ► Underestimation of VaR becomes less prevalent as forecasting horizon increases. ► Rolling-sampled FIGARCH parameters change less smoothly compared to GARCH models. ► Parameters' time-variant character is not entirely due to the news arrival process.