Our model is estimated and used to produce volatility forecasts at various horizons S&P 500 index-futures and three exchange rates, the DM/$, U/$ and
U/DM. The S&P results rst of all show that level shifts in S&P 500 volatility
do not account for the long memory feature. The fractional integration parameter
does decline when explicitly modeling the structural break, but remains signicantly
dierent from zero. Second, the day-of-the-week dummies show that volatility is on
average lower on Mondays and Tuesdays and higher on Fridays. This is an interesting
contrast with the U-shaped pattern found in daily squared returns, which
also attribute a higher volatility to Mondays and Tuesdays. Third, we nd convincing
evidence for the presence of a leverage eect in S&P volatility, in that negative
lagged returns signicantly increase volatility whereas positive returns do not aect
volatility at all. Incorporating these nonlinear features is important for out-of-sample forecasting as well.