Efficient Covariance Estimation for Asynchronous Noisy High‐Frequency Data

.  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 Ito 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.

[1]  N. Yoshida,et al.  On covariance estimation of non-synchronously observed diffusion processes , 2005 .

[2]  Lan Zhang.  Efficient Estimation of Stochastic Volatility Using Noisy Observations: A Multi-Scale Approach , 2004, math/0411397.

[3]  P. Gänssler.  Weak Convergence and Empirical Processes - A. W. van der Vaart; J. A. Wellner. , 1997 .

[4]  A. Lunde,et al.  Integrated Covariance Estimation using High-frequency Data in the Presence of Noise , 2006 .

[5]  Jean Jacod,et al.  Diffusions with measurement errors. II. Optimal estimators , 2001 .

[6]  J. Griffin,et al.  Covariance Measurement in the Presence of Non-Synchronous Trading and Market Microstructure Noise , 2009 .

[7]  An Econometric Analysis of Modulated Realised Covariance, Regression and Correlation in Noisy Diffusion Models , 2008 .

[8]  Lan Zhang.  Estimating Covariation: Epps Effect, Microstructure Noise , 2006 .

[9]  N. Shephard,et al.  Econometric Analysis of Realized Covariation: High Frequency Based Covariance, Regression, and Correlation in Financial Economics , 2004 .

[10]  Jean Jacod,et al.  Microstructure Noise in the Continuous Case: The Pre-Averaging Approach - JLMPV-9 , 2007 .

[11]  N. Shephard,et al.  Multivariate Realised Kernels: Consistent Positive Semi-Definite Estimators of the Covariation of Equity Prices with Noise and Non-Synchronous Trading , 2010 .

[12]  Neil Shephard,et al.  Designing Realised Kernels to Measure the Ex-Post Variation of Equity Prices in the Presence of Noise , 2008 .

[13]  A. V. D. Vaart,et al.  Asymptotic Statistics: Frontmatter , 1998 .

[14]  A. Shiryaev,et al.  Limit Theorems for Stochastic Processes , 1987 .

[15]  A. V. D. Vaart.  Asymptotic Statistics: Delta Method , 1998 .

[16]  Jean Jacod,et al.  Diffusions with measurement errors. I. Local Asymptotic Normality , 2001 .

[17]  Alessandro Palandri.  Consistent Realized Covariance for Asynchronous Observations Contaminated by Market Microstructure Noise , 2006 .

[18]  Jon A. Wellner,et al.  Weak Convergence and Empirical Processes: With Applications to Statistics , 1996 .

[19]  N. Shephard,et al.  Power and bipower variation with stochastic volatility and jumps , 2003 .

[20]  Jeffrey R. Russell,et al.  Realized covariation , realized beta , and microstructure noise , 2005 .

[21]  Lan Zhang,et al.  A Tale of Two Time Scales , 2003 .