Publication: Edgeworth expansions for spectral density estimates and studentized sample mean
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2001
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Cambridge University Press
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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Econometric Theory, 2001, 17, 3, p. 497-539