In this paper, we investigate the long memory properties for closing prices of three stock index futures markets. The FIGARCH (1, d, 1) and HYGARCH (1, d, 1) models with normal, Student-t, and skewed Student-t distributions for S&P500, Nasdaq100, and Dow Jones daily prices are estimated first. Then the value-at-risks are calculated by the estimated models. The empirical results show that for the three stock index futures, the HYGARCH (1, d, 1) models with skewed Student-t distribution perform better based on the Kupiec LR tests. In particular, for the S&P500 and Nasdag 100 futures prices.
Physica A: Statistical Mechanics and its Applications,366(1),437-448