Effects of Non-normality and Dependence on the Precision of Variance Estimates Using High Freqeuncy Data

• 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): Jeffrey Russell*+ and Xuezheng Bai and George Tiao
• Affiliation(s): University of Chicago and University of Chicago and University of Chicago
• Keywords: volatility ; high frequency data ; microstructure

Abstract

Volatility is central to financial theory. In practice, volatility is not directly observed and must be estimated. Historically, the sampling frequency was driven by data availability--first monthly, then weekly and daily. Now, we have at our disposal ultra high frequency data sets containing potentially 1000s of observations per day. Merton 's (1980) seminal work suggests that as the sampling interval approaches zero, arbitrarily precise volatility estimates can be obtained. Realistically, however, the limiting case is not attainable since the sampling frequency cannot be any higher than transaction by transaction. We derive analytical expression for the precision of volatility estimates as a function of the prominent high frequency data characteristics, including leptokurtosis, autocorrelation in the returns, deterministic patterns, and volatility clustering in intra-day variance. Simulations are presented to explore the efficiency of some maximum likelihood estimates. We find that large amounts of high frequency data do not necessarily translate into very precise estimates. Our results provide a measure of the usefulness of high frequency data in estimating volatility.