The comparison of forecasting performance of historical volatility versus realized volatility

When forecasting stock market volatility with a standard volatility method (GARCH), it is common that the forecast evaluation criteria often suggests that the realized volatility (the sum of squared high-frequency returns) has a better prediction performance compared to the historical volatility (extracted from the close-to-close return). Since many extensions of the GARCH model have been developed, we follow the previous works to compare the historical volatility with many new GARCH family models (i.e., EGARCH, TGARCH, and APARCH model) and realized volatility with the ARMA model. Our analysis is based on the S&P 500 index from August 1st, 2018 to February 1st, 2019 (127 trading days), and the data has been separated into an estimation period (90 trading days) and an evaluation period (37 trading days). In the evaluation period, by taking realized volatility as the proxy of the true volatility, our empirical result shows that the realized volatility with ARMA model provides more accurate predictions, compared to the historical volatility with the GARCH family models