#07-40
Roughing It Up: Including Jump Components in the Measurement,
Modeling and Forecasting of Return Volatility
Torben G. Andersen, Tim Bollerslev and Francis X. Diebold, August 2005
Abstract: A rapidly growing literature has documented important improvements in financial return volatility
measurement and forecasting via use of realized variation measures constructed from high-frequency returns
coupled with simple modeling procedures. Building on recent theoretical results in Barndorff-Nielsen and
Shephard (2004a, 2005) for related bi-power variation measures, the present paper provides a practical and
robust framework for non-parametrically measuring the jump component in asset return volatility. In an
application to the DM/$ exchange rate, the S&P500 market index, and the 30-year U.S. Treasury bond yield,
we find that jumps are both highly prevalent and distinctly less persistent than the continuous sample path
variation process. Moreover, many jumps appear directly associated with specific macroeconomic news
announcements. Separating jump from non-jump movements in a simple but sophisticated volatility
forecasting model, we find that almost all of the predictability in daily, weekly, and monthly return volatilities
comes from the non-jump component. Our results thus set the stage for a number of interesting future
econometric developments and important financial applications by separately modeling, forecasting, and
pricing the continuous and jump components of the total return variation process.
Keywords: Continuous-time methods; jumps; quadratic variation; realized volatility; bi-power variation; highfrequency data; volatility forecasting; macroeconomic news; HAR-RV model; HAR-RV-CJ model
JEL classifications: C1, G1
