We find that 1-day-ahead volatility forecasts from the best nonlinear
model improve upon those from a linear ARFIMA model on all evaluation
criteria considered. For example, the R2 from a regression of realized volatility on
the volatility forecast increases from 42.1% to 46.1%. For the exchange rates the
leverage eect is less important, as expected, but incorporating nonlinearities still
improves the in-sample t and out-of-sample forecast performance. For the U/$, for
example, the R2 from a regression of realized volatility on the 1-day-ahead volatility
forecast increases substantially from 36.6% to 55.4%.