Premium
Efficient Covariance Estimation for Asynchronous Noisy High‐Frequency Data
Author(s) -
BIBINGER MARKUS
Publication year - 2011
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2010.00712.x
Subject(s) - mathematics , estimator , covariance , rate of convergence , efficient estimator , delta method , covariance function , statistics , minimum variance unbiased estimator , computer science , computer network , channel (broadcasting)
. We focus on estimating the integrated covariance of log‐price processes in the presence of market microstructure noise. We construct a consistent asymptotically unbiased estimator for the quadratic covariation of two Itô processes in the case where high‐frequency asynchronous discrete returns under market microstructure noise are observed. This estimator is based on synchronization and multi‐scale methods and attains the optimal rate of convergence. A lower bound for the rate of convergence is derived from the local asymptotic normality property of the simpler parametric model with equidistant and synchronous observations. A Monte Carlo study analyses the finite sample size characteristics of our estimator.