Content horizons for conditional variance forecasts

Using realized variance to estimate daily conditional variance of financial returns, we compare forecasts of daily variance from standard GARCH and FIGARCH models estimated by Quasi-Maximum Likelihood (QML), and from projections on past realized volatilities obtained from high-frequency data. We consider horizons extending to 30 trading days. The forecasts are compared with the unconditional sample variance of daily returns treated as a predictor of daily variance, allowing us to estimate the maximum horizon at which conditioning information has exploitable value for variance forecasting. With foreign exchange return data (DM/$US and Yen/$US), we find evidence of forecasting power at horizons of up to 30 trading days, on each of two financial returns series. We also find some evidence that the result of (e.g.) Bollerslev and Wright [Bollerslev, T., & Wright, J. H. (2001) High-frequency data, frequency domain inference, and volatility forecasting. Review of Economics and Statistics, 83, 596-602], that projections on past realized variance provide better one-step forecasts than the QML-GARCH and -FIGARCH forecasts, appears to extend to longer horizons up to around 10 to 15 trading days. At longer horizons, there is less to distinguish the forecast methods, but the evidence does suggest positive forecast content at 30 days for various forecast types.