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EDGEWORTH EXPANSIONS FOR SPECTRAL DENSITY ESTIMATES AND STUDENTIZED SAMPLE MEAN

  • Carlos Velasco (a1) and Peter M. Robinson (a2)
    • Published online: 27 July 2001
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.

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Corresponding author
Address correspondence to: Carlos Velasco, Departamento de Estadística y Econometría, Universidad Carlos III de Madrid, Avenida de la Universidad 30, E-28911 Leganés (Madrid), Spain.
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Econometric Theory
  • ISSN: 0266-4666
  • EISSN: 1469-4360
  • URL: /core/journals/econometric-theory
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