AbstractWe use an international dataset on 5‐min interval intraday data covering nine leading markets and regions to construct measures of realized volatility, realized jumps, realized skewness, and realized kurtosis of returns of international Real Estate Investment Trusts (REITs) over the daily period of September 2008 to August 2020. We study out‐of‐sample the predictive value of realized skewness and realized kurtosis for realized volatility over and above realized jumps, where we also differentiate between measures of “good” realized volatility and “bad” realized volatility. We find that realized skewness and realized kurtosis significantly improve forecasting performance at a daily, weekly, and monthly forecast horizon and that their contribution to forecasting performance outweighs in terms of significance the contribution of realized jumps. Our results have important implications for investors and policymakers.