Estimating Covariation: Epps Effect, Microstructure Noise

Abstract

This paper is about how to estimate the integrated covariance _T of two price processes over a fixed time horizon [0, T], when the observations about X and Y are contaminated and when such noisy observations are at discrete, but not synchronized, times. We show that the usual covariance estimator is biased, and the size of the bias is more pronounced for less liquid assets. We also provide optimal sampling frequency which balances the tradeoff between the bias and various sources of stochastic error terms, including nonsynchronous trading, microstructure noise, and time discretization.

Keywords: Bias-variance tradeoff, Epps effect, High frequency data, Market Microstructure, Martingale, Nonsynchronous trading, Realized covariance, Realized variance

JEL Classification: C14, C40, C51