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FAST CONVERGENCE RATES IN ESTIMATING LARGE VOLATILITY MATRICES USING HIGH-FREQUENCY FINANCIAL DATA

Published online by Cambridge University Press:  03 January 2013

Minjing Tao ,
Yazhen Wang  and
Xiaohong Chen
Minjing Tao
Affiliation:
University of Wisconsin-Madison
Yazhen Wang*
Affiliation:
University of Wisconsin-Madison
Xiaohong Chen
Affiliation:
Yale University
*
*Address correspondence to Yazhen Wang, Dept. of Statistics, University of Wisconsin, Medical Science Center, 1300 University Ave., Madison, WI 53706, USA; e-mail: [email protected].
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Abstract

Financial practices often need to estimate an integrated volatility matrix of a large number of assets using noisy high-frequency data. Many existing estimators of a volatility matrix of small dimensions become inconsistent when the size of the matrix is close to or larger than the sample size. This paper introduces a new type of large volatility matrix estimator based on nonsynchronized high-frequency data, allowing for the presence of microstructure noise. When both the number of assets and the sample size go to infinity, we show that our new estimator is consistent and achieves a fast convergence rate, where the rate is optimal with respect to the sample size. A simulation study is conducted to check the finite sample performance of the proposed estimator.

Type
ARTICLES
Information
Econometric Theory , Volume 29 , Issue 4 , August 2013 , pp. 838 - 856
Copyright
Copyright © Cambridge University Press 2012 

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