As the use of intraday high-frequency data in financial markets increases, various studies have been conducted to improve future volatility forecasting performance by combining realized volatility (RV) measured from such data with the heterogeneous autoregressive (HAR) model. This study measured realized volatility using intraday high-frequency data from the KOSPI, constructed heterogeneous autoregressive models that newly incorporate realized skewness and realized kurtosis, and verified the forecasting performance of future volatility based on these models. For the study, we employed improved methods that address problems identified in prior research during the process of measuring realized volatility and nonparametrically separating discontinuous jump components from realized volatility. The main findings of this study are summarized as follows. First, the heterogeneous autoregressive model reflecting past-period realized volatility in the Korean stock market demonstrates high explanatory power for changes in future realized volatility, and separating the continuous component and discontinuous jump component of realized volatility—which possess different properties—and applying them to the model is useful for improving explanatory power for changes in future realized volatility. Second, the HAR-RV model that newly incorporates realized skewness and realized kurtosis shows clear evidence of improving explanatory power and forecasting performance for future realized volatility. That is, realized skewness and realized kurtosis contain additional information that can better explain changes in short-term and long-term volatility according to the characteristics of heterogeneous investors, and they are key variables that can improve explanatory power and predictive power for future volatility. Furthermore, the usefulness of these new explanatory variables holds regardless of the previously known volatility leverage effect and the characteristics of intraday return volatility.