Time-varying variance and skewness in realized volatility measures

We propose new empirical models to capture the dynamics of the variance and skewness in realized volatility measures. We find that time-variation in variance and skewness of realized measures is a key empirical feature, even after accounting for well-known, stylized facts such as long-memory-type persistence and large incidental observations. Using a broad range of 89 US stocks across different sectors over 2001–2019, we show that these are not incidental phenomena of a few stocks but are widely shared. Accounting for dynamics in the variance and skewness of realized measures results in significantly better in-sample fit and out-of-sample unconditional density and quantile forecasts.