Efficient Covariance Estimation for Asynchronous Noisy High-Frequency Data

Efficient Covariance Estimation for Asynchronous Noisy High-Frequency Data

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Article ID: iaor201112541
Volume: 38
Issue: 1
Start Page Number: 23
End Page Number: 45
Publication Date: Mar 2011
Journal: Scandinavian Journal of Statistics
Authors:
Keywords: statistics: distributions, stochastic processes, heuristics
Abstract:

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.

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