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Edgeworth expansions for spectral density estimates and studentized sample mean

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  • Robinson, Peter M.
  • Velasco, Carlos

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.

Suggested Citation

  • Robinson, Peter M. & Velasco, Carlos, 2000. "Edgeworth expansions for spectral density estimates and studentized sample mean," LSE Research Online Documents on Economics 2148, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:2148
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    References listed on IDEAS

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    1. Taniguchi, Masanobu & Puri, Madan L., 1996. "Valid Edgeworth Expansions of M-Estimators in Regression Models with Weakly Dependent Resfduals," Econometric Theory, Cambridge University Press, vol. 12(2), pages 331-346, June.
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    More about this item

    Keywords

    Edgeworth expansions; nonparametric spectral estimates; stationary Gaussian series; studentized sample mean; bandwidth choice.;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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