Edgeworth Expansions for Spectral Density Estimates and Studentized Sample Mean - (Now Published in Economic Theory, 17 (2001), Pp.497-539.

39 Pages Posted: 21 Jul 2008

See all articles by Carlos Velasco

Carlos Velasco

Universidad Carlos III de Madrid - Department of Economics

Date Written: May 2000

Abstract

We establish valid Edgeworth expansions for the distribution of smoothed nonparametric spectral estimates, and of studentized versions of linear statistics such as the same 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 a feasible rule of bandwidth choice.

JEL Classification: C13, C14

Suggested Citation

Velasco, Carlos, Edgeworth Expansions for Spectral Density Estimates and Studentized Sample Mean - (Now Published in Economic Theory, 17 (2001), Pp.497-539. (May 2000). LSE STICERD Research Paper No. EM390. Available at SSRN: https://ssrn.com/abstract=1162583

Carlos Velasco

Universidad Carlos III de Madrid - Department of Economics ( email )

Calle Madrid 126
Getafe, 28903
Spain
+34-91 6249646 (Phone)
+34-91 6249875 (Fax)

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