This paper compares the performance of long-memory models (FIGARCH) with
short-memory models (GARCH) in forecasting volatility for calculating
value-at-risk (VaR) and expected shortfall (ES) for multiple periods ahead
for six emerging markets stock indices. We used daily data from 1999 to 2014
and an adaptation of the Monte Carlo simulation to estimate VaR and ES
forecasts for
multiple steps ahead (1, 10 and 20 days ), using FIGARCH
and GARCH models for four errors distributions. The results suggest that, in
general, the FIGARCH models improve the accuracy of forecasts for longer
horizons; that the error distribution used may influence the decision about
the best model; and that only for FIGARCH models the occurrence of
underestimation of the true VaR is less frequent with increasing time
horizon. However, the results suggest that rolling sampled estimated FIGARCH
parameters change less smoothly over time compared to the GARCH
models.
Semiparametric GARCH Models with Long Memory Applied to Value at Risk and Expected Shortfall