Modelling and Forecasting Realized Volatility

• Activity Number: 268
• Type: Invited
• Date/Time: Wednesday, August 14, 2002 : 8:30 AM to 10:20 AM
• Sponsor: Business & Economics Statistics Section*
• Author(s): Torben Andersen*+ and Francis Diebold and Tim Bollerslev
• Affiliation(s): Northwestern University and University of Pennsylvania and Duke University
• Keywords: realized volatility ; continuous-time methods ; volatility forecasting ; density forecasting ; long memory ; high-frequency data

Abstract

We provide a general framework for integration of high-frequency intraday data into the measurement, modeling, and forecasting of daily and lower frequency return volatilities and return distributions. Building on continuous-time arbitrage-free price processes and quadratic variation theory, we develop the links between realized volatility and the conditional covariance matrix. Next, using intradaily observations for the DM/ Dollar and Yen /Dollar spot exchange rates, we find that forecasts from a simple long-memory Gaussian vector autoregression for the log daily realized volatilities often perform admirably compared to a variety of popular daily ARCH and more complex high-frequency models. Moreover, the vector autoregressive volatility forecast, coupled with a parametric lognormal-normal mixture distribution produces well-calibrated return density forecasts and, correspondingly, accurate quantile predictions.