Estimating the Quadratic Covariation Matrix from Noisy Observations: Local Method of Moments and Efficiency

Abstract

An efficient estimator is constructed for the quadratic covariation or integrated covolatility matrix of a multivariate continuous martingale based on noisy and non-synchronous observations under high-frequency asymptotics. Our approach relies on an asymptotically equivalent continuous-time observation model where a local generalised method of moments in the spectral domain turns out to be optimal. Asymptotic semiparametric efficiency is established in the Cramer-Rao sense. Main findings are that non-synchronicity of observation times has no impact on the asymptotics and that major efficiency gains are possible under correlation. Simulations illustrate the finite-sample behaviour.

Keywords: adaptive estimation, asymptotic equivalence, asynchronous observations, integrated covolatility matrix, quadratic covariation, semiparametric efficiency, microstructure noise, spectral estimation

JEL Classification: C13, C32, G10