Forecasting S&P 500 volatility: Long memory, level shifts, leverage effects, day-of-the-week seasonality, and macroeconomic

We evaluate the forecasting performance of time series models for realized volatility, which accommodate long memory, level shifts, leverage effects, day-of-the-week and holiday effects, as well as macroeconomic news announcements. Applying the models to daily realized volatility for the S&P 500 futures index, we find that explicitly accounting for these stylized facts of volatility improves out-of-sample forecast accuracy for horizons up to 20 days ahead. Capturing the long memory feature of realized volatility by means of a flexible high-order AR-approximation instead of a parsimonious but stringent fractionally integrated specification also leads to improvements in forecast accuracy, especially for longer horizon forecasts.