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On Sample Skewness and Kurtosis

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  • Yong Bao

Abstract

It is well documented in the literature that the sample skewness and excess kurtosis can be severely biased in finite samples. In this paper, we derive analytical results for their finite-sample biases up to the second order. In general, the bias results depend on the cumulants (up to the sixth order) as well as the dependency structure of the data. Using an AR(1) process for illustration, we show that a feasible bias-correction procedure based on our analytical results works remarkably well for reducing the bias of the sample skewness. Bias-correction works reasonably well also for the sample kurtosis under some moderate degree of dependency. In terms of hypothesis testing, bias-correction offers power improvement when testing for normality, and bias-correction under the null provides also size improvement. However, for testing nonzero skewness and/or excess kurtosis, there exist nonnegligible size distortions in finite samples and bias-correction may not help.

Suggested Citation

  • Yong Bao, 2013. "On Sample Skewness and Kurtosis," Econometric Reviews, Taylor & Francis Journals, vol. 32(4), pages 415-448, December.
  • Handle: RePEc:taf:emetrv:v:32:y:2013:i:4:p:415-448
    DOI: 10.1080/07474938.2012.690665
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    File URL: http://hdl.handle.net/10.1080/07474938.2012.690665
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    Cited by:

    1. Mutschler, Willi, 2015. "Note on Higher-Order Statistics for the Pruned-State-Space of nonlinear DSGE models," Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 113138, Verein für Socialpolitik / German Economic Association.
    2. Mutschler, Willi, 2015. "Identification of DSGE models—The effect of higher-order approximation and pruning," Journal of Economic Dynamics and Control, Elsevier, vol. 56(C), pages 34-54.
    3. Willi Mutschler, 2015. "Higher-order statistics for DSGE models," CQE Working Papers 4315, Center for Quantitative Economics (CQE), University of Muenster.

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