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High-dimensional volatility matrix estimation via wavelets and thresholding

Fryzlewicz, P. (2013) High-dimensional volatility matrix estimation via wavelets and thresholding. Biometrika . ISSN 0006-3444

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Abstract

We propose a locally stationary linear model for the evolution of high-dimensional financial returns, where the time-varying volatility matrix is modelled as a piecewise constant function of time. We introduce a new wavelet-based technique for estimating the volatility matrix, which 10 combines four ingredients: a Haar wavelet decomposition, variance stabilization of the Haar coefficients via the Fisz transform prior to thresholding, a bias correction, and extra time-domain thresholding, soft or hard. Under the assumption of sparsity, we demonstrate the interval-wise consistency of the proposed estimators of the volatility matrix and its inverse in the operator norm, with rates which adapt to the features of the target matrix. We also propose a version of 15 the estimators based on the polarization identity, which permits a more precise derivation of the thresholds. We discuss the practicalities of the algorithm, including parameter selection and how to perform it online. A simulation study shows the benefits of the method, which is illustrated using a stock index portfolio.

Item Type: Article
Official URL: http://biomet.oxfordjournals.org/
Additional Information: © 2013 Biometrika Trust
Library of Congress subject classification: H Social Sciences > HA Statistics
Q Science > QA Mathematics
Sets: Departments > Statistics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 07 Aug 2013 10:54
URL: http://eprints.lse.ac.uk/51499/

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