We devise a new high-frequency covariance matrix estimator based on price durations which is guaranteed to be positive-definite. Both non-parametric and parametric versions are proposed. A comprehensive Monte Carlo simulation shows that this class of estimators are less biased, more efficient,...

This note contains the supplements to Li and Linton (2019). Section A contains extensive simulation studies. Section B presents the methodology and a detailed numerical algorithm to select the tuning parameters. Section C presents additional empirical studies. Section D contains all mathematical...