The most important nonlinearities are the leverage eect for the S&P 500 index,
and the leverage eect as well as the day-of-the-week eects for the exchange rates.
The best way to incorporate the eects of lagged daily returns is to include them
as exogenous regressors, i.e. outside the long memory lter. Not important for the
forecast performance is allowing the persistence of shocks to depend on the level of
volatility, and modeling the level shifts for the S&P 500 index.