Effects of non-normality and dependence on the precision of variance estimates using high-frequency financial data

Abstract

Volatility (or variance) is central to financial theory. In practice, variance is not directly observed and must be estimated. Merton's seminal work in 1980 suggests that as the sampling interval approaches zero arbitrarily precise estimates of the variance can be obtained. In this spirit, numerous studies have suggested using high-frequency financial data to estimate the variance of financial asset returns. Realistically the sampling frequency cannot be any higher than transaction by transaction. We examine the precision of variance estimates that use high-frequency data, and find that large amounts of high- frequency data do not necessarily translate into precise estimates of the volatility. Specifically, the precision of variance estimates can vary substantially across different financially assets depending on the degree of dependence and kurtosis in the returns. This suggests that the advantage of using high-frequency data to estimate the variance may vary greatly across different assets. Furthermore, results on the lack of robustness of variance estimates with respect to non-normality and dependence can also be applied to studying process data in quality control and related problems.