"Good" and "bad" volatilities: a realized semivariance GARCH approach

In this article, we explore the realized semivariation measures using high-frequency intraday data within the framework of realized semivariance GARCH by taking an in-depth look. We derive general theoretical expressions for moment conditions of returns and realized semivariation measures, providing a convenient approach to investigate the statistical properties of realized semivariation dynamics. Notably, the introduction of threshold effects in the model reveals several intriguing empirical findings. One significant discovery is that during a substantial decline in returns, the negative realized semivariance exerts a more influential impact on future volatility compared to its positive counterpart. We further examine the forecasting performance under a realized semivariance heterogeneous autoregression environment. The results demonstrate that the inclusion of thresholds and the adoption of an optimal threshold level generally enhance the accuracy of volatility forecasting.