Department of Economics and Business Economics

Flat-Top Realized Kernel Estimation of Quadratic Covariation with Non-Synchronous and Noisy Asset Prices

Research output: Working paper/Preprint Working paperpeer-review

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Flat-Top Realized Kernel Estimation of Quadratic Covariation with Non-Synchronous and Noisy Asset Prices. / Varneskov, Rasmus T.

Aarhus : Institut for Økonomi, Aarhus Universitet, 2013.

Research output: Working paper/Preprint Working paperpeer-review

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@techreport{4200721e0c184d6bba1a2ae2bee399b0,
title = "Flat-Top Realized Kernel Estimation of Quadratic Covariation with Non-Synchronous and Noisy Asset Prices",
abstract = "This paper extends the class of generalized at-top realized kernels, introduced in Varneskov (2011), to the multivariate case, where quadratic covariation of non-synchronously observed asset prices is estimated in the presence of market microstructure noise that is allowed to exhibit serial dependence and to be correlated with the efficient price process. Estimators in this class are shownto posses desirable statistical properties such as consistency, asymptotic normality, and asymptotic unbiasedness at an optimal n^(1/4)-convergence rate. A finite sample correction based on projections of symmetric matrices ensures positive (semi-)definiteness without altering asymptotic properties of the class of estimators. The finite sample correction admits non-linear transformations of the estimated covariance matrix such as correlations and realized betas, and it can be used in portfolio optimization problems. These transformations are all shown to inherit the desirable asymptotic properties of the generalized at-top realized kernels. A simulation study shows that the class of estimators has a superior finite sample tradeoff between bias and root mean squared error relative to competing estimators. Lastly, two small empirical applications to high frequency stock market data illustrate the bias reduction relative to competing estimators in estimating correlations, realized betas, and mean-variance frontiers, as well as the use of the new estimators in the dynamics of hedging.",
keywords = "Bias Reduction, Nonparametric Estimation, Market Microstructure Noise, Portfolio Optimization, Quadratic Covariation, Realized Beta",
author = "Varneskov, {Rasmus T.}",
year = "2013",
language = "English",
publisher = "Institut for {\O}konomi, Aarhus Universitet",
type = "WorkingPaper",
institution = "Institut for {\O}konomi, Aarhus Universitet",

}

RIS

TY - UNPB

T1 - Flat-Top Realized Kernel Estimation of Quadratic Covariation with Non-Synchronous and Noisy Asset Prices

AU - Varneskov, Rasmus T.

PY - 2013

Y1 - 2013

N2 - This paper extends the class of generalized at-top realized kernels, introduced in Varneskov (2011), to the multivariate case, where quadratic covariation of non-synchronously observed asset prices is estimated in the presence of market microstructure noise that is allowed to exhibit serial dependence and to be correlated with the efficient price process. Estimators in this class are shownto posses desirable statistical properties such as consistency, asymptotic normality, and asymptotic unbiasedness at an optimal n^(1/4)-convergence rate. A finite sample correction based on projections of symmetric matrices ensures positive (semi-)definiteness without altering asymptotic properties of the class of estimators. The finite sample correction admits non-linear transformations of the estimated covariance matrix such as correlations and realized betas, and it can be used in portfolio optimization problems. These transformations are all shown to inherit the desirable asymptotic properties of the generalized at-top realized kernels. A simulation study shows that the class of estimators has a superior finite sample tradeoff between bias and root mean squared error relative to competing estimators. Lastly, two small empirical applications to high frequency stock market data illustrate the bias reduction relative to competing estimators in estimating correlations, realized betas, and mean-variance frontiers, as well as the use of the new estimators in the dynamics of hedging.

AB - This paper extends the class of generalized at-top realized kernels, introduced in Varneskov (2011), to the multivariate case, where quadratic covariation of non-synchronously observed asset prices is estimated in the presence of market microstructure noise that is allowed to exhibit serial dependence and to be correlated with the efficient price process. Estimators in this class are shownto posses desirable statistical properties such as consistency, asymptotic normality, and asymptotic unbiasedness at an optimal n^(1/4)-convergence rate. A finite sample correction based on projections of symmetric matrices ensures positive (semi-)definiteness without altering asymptotic properties of the class of estimators. The finite sample correction admits non-linear transformations of the estimated covariance matrix such as correlations and realized betas, and it can be used in portfolio optimization problems. These transformations are all shown to inherit the desirable asymptotic properties of the generalized at-top realized kernels. A simulation study shows that the class of estimators has a superior finite sample tradeoff between bias and root mean squared error relative to competing estimators. Lastly, two small empirical applications to high frequency stock market data illustrate the bias reduction relative to competing estimators in estimating correlations, realized betas, and mean-variance frontiers, as well as the use of the new estimators in the dynamics of hedging.

KW - Bias Reduction, Nonparametric Estimation, Market Microstructure Noise, Portfolio Optimization, Quadratic Covariation, Realized Beta

M3 - Working paper

BT - Flat-Top Realized Kernel Estimation of Quadratic Covariation with Non-Synchronous and Noisy Asset Prices

PB - Institut for Økonomi, Aarhus Universitet

CY - Aarhus

ER -