Moderate and Extreme Volatility: Do the Magnitude of Returns Matter for Forecasting?

This paper proposes a novel decomposition of realized volatility (RV) into moderate and extreme realized volatility estimates. These estimates behave like long and short term components of volatility, and are very different from either realized semi-variance or the continuous and jump components of volatility. Within the standard linear HAR framework, a forecast comparison exercise using index returns shows that employing the new decomposition leads to forecasts that are often superior to the competing forecasts based on existing realized measures.