High-frequency volatility combine forecast evaluations: An empirical study for DAX

This study aims to examine the benefits of combining realized volatility, higher power variation volatility and nearest neighbour truncation volatility in the forecasts of financial stock market of DAX. A structural break heavy-tailed heterogeneous autoregressive model under the heterogeneous market hypothesis specification is employed to capture the stylized facts of high-frequency empirical data. Using selected averaging forecast methods, the forecast weights are assigned based on the simple average, simple median, least squares and mean square error. The empirical results indicated that the combination of forecasts in general shown superiority under four evaluation criteria regardless which proxy is set as the actual volatility. As a conclusion, we summarized that the forecast performance is influenced by three factors namely the types of volatility proxy, forecast methods (individual or averaging forecast) and lastly the type of actual forecast value used in the evaluation criteria.