# Per Mykland: The Algebra of Two Scales Estimation - High Frequency Estimation that is Robust to Sampling Times

Prof Per Mykland (University of Chicago) will give a seminar in the lunch area, 8th floor Niels Henrik Abels hus at 14:15.

**Title:** The Algebra of Two Scales Estimation - High Frequency Estimation that is Robust to Sampling Times

**Abstract: **In this paper, we show a new algebraic property of two scales estimation in high frequency data, under which the effect of sampling times is cancelled to high order. This is a particular robustness property of the two scales estimator. In general, irregular times can cause problems in estimators based on equidistant observation (trading or quote) times.

The new algebraic property can be combined with pre-averaging, and also presents a solution for handling asynchronously observed multivariate data. In connection with this development, we use the algebraic approach to define a version of two scales estimation which has no edge effect in

microstructure noise. Finally, the paper develops a central limit theory.