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

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  • Peter M Robinson
  • Carlos Velasco

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.

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File URL: http://sticerd.lse.ac.uk/dps/em/em390.pdf
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Bibliographic Info

Paper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /2000/390.

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Date of creation: May 2000
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Handle: RePEc:cep:stiecm:/2000/390

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Web page: http://sticerd.lse.ac.uk/_new/publications/default.asp

Related research

Keywords: Edgeworth expansions; nonparametric spectral estimates; stationary Gaussian series; studentized sample mean; bandwidth choice.;

References

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  1. repec:cup:etheor:v:12:y:1996:i:2:p:331-46 is not listed on IDEAS
  2. Robinson, P M, 1991. "Automatic Frequency Domain Inference on Semiparametric and Nonparametric Models," Econometrica, Econometric Society, vol. 59(5), pages 1329-63, September.
  3. Taniguchi, Masanobu, 1987. "Validity of Edgeworth expansions of minimum contrast estimators for Gaussian ARMA processes," Journal of Multivariate Analysis, Elsevier, vol. 21(1), pages 1-28, February.
  4. Robinson, P. M., 1995. "The approximate distribution of nonparametric regression estimates," Statistics & Probability Letters, Elsevier, vol. 23(2), pages 193-201, May.
  5. Phillips, P C B, 1980. "Finite Sample Theory and the Distributions of Alternative Estimators of the Marginal Propensity to Consume," Review of Economic Studies, Wiley Blackwell, vol. 47(1), pages 183-224, January.
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Cited by:
  1. Peter C.B. Phillips & Yixiao Sun & Sainan Jin, 2005. "Improved HAR Inference," Cowles Foundation Discussion Papers 1513, Cowles Foundation for Research in Economics, Yale University.

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