Statistical Methods in Finance 2022

June 28 to July 2, 2022


Nonparametric Observed Standard Errors for High Frequency Data

By Per Mykland
University of Chicago

High frequency financial data has become an essential component of the digital world, giving rise to an increasing number of estimators. However, it is hard to reliably assess the uncertainty of such estimators. The Observed Asymptotic Variance (observed AVAR) is a non-parametric (squared) standard error for high- frequency-based estimators. We have earlier developed such an AVAR with time-discretization and two tuning parameters (per dimension). The current paper shows that these two parameters are confounded, and one can move to a single tuning parameter. This is shown by passing to continuous time (which is natural since observations are usually irregularly spaced). We show that the new time-continuous observed AVAR is a limit of the original observed AVAR. We also obtain a central limit theory for the new time-continuous observed AVAR, and the latter permits a sharper definition of our standard error. The device is related to observed information in likelihood theory, but in this case it is non-parametric and uses the high-frequency data structure. [With Lan Zhang, University of Illinois at Chicago.]