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HIGHER-ORDER ACCURATE, POSITIVESEMIDEFINITE ESTIMATION OF LARGE-SAMPLE COVARIANCEAND SPECTRAL DENSITY MATRICES

Published online by Cambridge University Press:  03 March 2011

Dimitris N. Politis
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Abstract

A new class of large-sample covariance and spectraldensity matrix estimators is proposed based on thenotion of flat-top kernels. The new estimators areshown to be higher-order accurate when higher-orderaccuracy is possible. A discussion on kernel choiceis presented as well as a supporting finite-samplesimulation. The problem of spectral estimation undera potential lack of finite fourth moments is alsoaddressed. The higher-order accuracy of flat-topkernel estimators typically comes at the sacrificeof the positive semidefinite property. Nevertheless,we show how a flat-top estimator can be modified tobecome positive semidefinite (even strictly positivedefinite) while maintaining its higher-orderaccuracy. In addition, an easy (and consistent)procedure for optimal bandwidth choice is given;this procedure estimates the optimal bandwidthassociated with each individual element of thetarget matrix, automatically sensing (and adaptingto) the underlying correlation structure.

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Type
Research Article
Information
Econometric Theory , Volume 27 , Issue 4 , August 2011 , pp. 703 - 744
Copyright
Copyright © Cambridge University Press 2011

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Footnotes

This research was partially supported by NSFgrants SES-04-18136 and DMS-07-06732. Many thanksare due to Arthur Berg and Tucker McElroy fornumerous helpful interventions, to Peter Robinsonfor a critical reading and suggestions of some keyearly references, and to Dimitrios Gatzouras forhis help with the proof of Lemma B.1. The S+software for the practical computation of thedifferent spectral density estimators was compiledwith the invaluable help of Isheeta Nargis andArif Dowla of www.stochasticlogic.com,and is now publicly available from www.math.ucsd.edu/∼politis/SOFT/SfunctionsFLAT-TOPS.html.Finally, the author is grateful to the co-editorand three anonymous reviewers for their insightfulsuggestions.

References

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