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Edgeworth expansions for spectral density estimates and studentized sample mean

Velasco, Carlos and Robinson, Peter M. (2001) Edgeworth expansions for spectral density estimates and studentized sample mean. Econometric Theory, 17 (3). pp. 497-539. ISSN 1469-4360

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Abstract

We establish valid Edgeworth expansions for the distribution of smoothed nonparametric spectral estimates, and of studentized versions of linear statistics such as the sample mean, where the studentization employs such a nonparametric spectral estimate. Particular attention is paid to the spectral estimate at zero frequency and, correspondingly, the studentized sample mean, to reflect econometric interest in autocorrelation-consistent or long-run variance estimation. Our main focus is on stationary Gaussian series, though we discuss relaxation of the Gaussianity assumption. Only smoothness conditions on the spectral density that are local to the frequency of interest are imposed. We deduce empirical expansions from our Edgeworth expansions designed to improve on the normal approximation in practice and also deduce a feasible rule of bandwidth choice.

Item Type: Article
Official URL: http://uk.cambridge.org/journals/ect/
Additional Information: © 2001 Cambridge University Press
Library of Congress subject classification: H Social Sciences > HB Economic Theory
Sets: Collections > Economists Online
Departments > Economics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 15 Feb 2008
URL: http://eprints.lse.ac.uk/315/

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