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Extended Neyman smooth goodness-of-fit tests, applied to competing heavy-tailed distributions

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  • McCulloch, J. Huston
  • Percy, E. Richard

Abstract

A simplified version of the Neyman (1937) “Smooth” goodness-of-fit test is extended to account for the presence of estimated model parameters, thereby removing overfitting bias. Using a Lagrange Multiplier approach rather than the Likelihood Ratio statistic proposed by Neyman greatly simplifies the calculations. Polynomials, splines, and the step function of Pearson’s test are compared as alternative perturbations to the theoretical uniform distribution. The extended tests have negligible size distortion and more power than standard tests. The tests are applied to competing symmetric leptokurtic distributions with US stock return data. These are generally rejected, primarily because of the presence of skewness.

Suggested Citation

  • McCulloch, J. Huston & Percy, E. Richard, 2013. "Extended Neyman smooth goodness-of-fit tests, applied to competing heavy-tailed distributions," Journal of Econometrics, Elsevier, vol. 172(2), pages 275-282.
    • Handle: RePEc:eee:econom:v:172:y:2013:i:2:p:275-282
    DOI: 10.1016/j.jeconom.2012.08.018
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    References listed on IDEAS

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    Cited by:

    1. Marc S. Paolella, 2016. "Stable-GARCH Models for Financial Returns: Fast Estimation and Tests for Stability," Econometrics, MDPI, vol. 4(2), pages 1-28, May.
    2. Ivan Korolev, 2018. "A Consistent Heteroskedasticity Robust LM Type Specification Test for Semiparametric Models," Papers 1810.07620, arXiv.org, revised Nov 2019.
    3. Paolella, Marc S., 2017. "Asymmetric stable Paretian distribution testing," Econometrics and Statistics, Elsevier, vol. 1(C), pages 19-39.

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    More about this item

    Keywords

    Stable distribution; Student t distribution; Generalized error distribution; Lagrange multiplier test;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions

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