Empirical Evaluation of Competing High-Frequency Estimators of Quadratic Variation

We propose methods for testing hypotheses about differences in bias, differences in error variance, and differences in the mean squared errors of competing estimators of quadratic variation computed using intradaily data. Our approach works under reasonably mild assumptions for members of a class of estimators that may be written as a quadratic form. We prove bootstrap limit theorems that facilitate the use of our tests with multiple hypothesis testing methodologies and investigate finite-sample properties under a range of situations using simulations. We apply our approach to a comparison of competing volatility estimators for a large cross-section of the most liquid stocks traded on the New York Stock Exchange and find that noise-robust volatility estimators generate lower mean-squared errors than 5-min realized volatility for many stocks.