prices. We empirically assess efficiency gains in volatility estimation when using range-based estimators as opposed to … simple daily ranges and explore the use of these more efficient volatility measures as predictors of daily ranges. The array … forecasts are produced by a realized range based HAR model with a GARCH volatility-of-volatility component. …

of covariates as well as the smoothing parameters via cross-validation. We find that volatility forecastability is much … squared return prediction errors gives an adequate approximation of the unobserved realised conditional variance for both the …

the corresponding GARCH volatility function. The prediction of GARCH squares is facilitated by the ARMA structure and … of their dependent and volatile innovations. The volatility function of the ARMA innovations is shown to be the square of …