Statistics and Data Science Seminar
Professor Per Mykland
University of Chicago
A Gaussian Calculus for Inference from High Frequency Data
Abstract: In the econometric literature of high frequency data, it is often assumed that
one can carry out inference conditionally on the underlying volatility
processes. In other words, conditionally Gaussian systems are
considered. This is often referred to as the assumption of ``no leverage
effect". This is often a reasonable thing to do, as general estimators and
results can often be conjectured from considering the conditionally
Gaussian case. The purpose of this paper is to try to give some more structure
to the things one can do with the Gaussian assumption. We shall argue in the
following that there is a whole treasure chest of tools that
can be brought to bear on high frequency data problems in this case. We shall in
particular consider approximations involving locally constant volatility
processes, and develop a general theory for this approximation. As applications
of the theory, we propose an improved estimator of quarticity, an ANOVA for
processes with multiple regressors, and an estimator for error bars on the
Hayashi-Yoshida estimator of quadratic covariation.
Tea at 3:15pm
Wednesday April 18, 2007 at 3:30 PM in SEO 712