Calculated results of optimal d for FFD.

Knowledge of the key macroeconomic variables that influence stock volatility across capital sizes, styles, and sectors can provide clues for investment strategies and policy decisions. We use the GARCH-MIDAS model with feature selection to analyze Korean Benchmark Indices from 2009 to 2022. This study maximizes memory retention through an optimal fractional differentiated price series and uses an adaptive lasso penalty for feature selection. The housing price-sales index and realized volatility were consistently influential across most indices and sectors. The GARCH-MIDAS model, paired with these variables, significantly improves long-term stock volatility forecasts. This study underscores the need to monitor housing prices in South Korea because of their substantial effects on long-term stock volatility.