IDEAS home Printed from https://ideas.repec.org/p/zbw/fubsbe/20049.html
   My bibliography  Save this paper

Jarque-Bera test and its competitors for testing normality: A power comparison

Author

Listed:
  • Thadewald, Thorsten
  • Büning, Herbert

Abstract

For testing normality we investigate the power of several tests, first of all, the well known test of Jarque and Bera (1980) and furthermore the tests of Kuiper (1960) and Shapiro and Wilk (1965) as well as tests of Kolmogorov-Smirnov and Cramer-von Mises type. The tests on normality are based, first, on independent random variables (model I) and, second, on the residuals in the classical linear regression (model II). We investigate the exact critical values of the Jarque-Bera test and the Kolmogorov-Smirnov and Cramer-von Mises tests, in the latter case for the original and standardized observations where the unknown parameters u and o have to be estimated. The power comparison is carried out via Monte Carlo simulation assuming the model of contaminated normal distributions with varying parameters u and o and different proportions of contamination. It turns out that for the Jarque-Bera test the approximation of critical values by the chi-square distribution does not work very well. The test is superior in power to its competitors for symmetric distributions with medium up to long tails and for slightly skewed distributions with long tails. The power of the Jarque-Bera test is poor for distributions with short tails, especially if the shape is bimodal, sometimes the test is even biased. In this case a modification of the Cramer-von Mises test or the Shapiro-Wilk test may be recommended.

Suggested Citation

  • Thadewald, Thorsten & Büning, Herbert, 2004. "Jarque-Bera test and its competitors for testing normality: A power comparison," Discussion Papers 2004/9, Free University Berlin, School of Business & Economics.
  • Handle: RePEc:zbw:fubsbe:20049
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/49919/1/668828234.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. Muchlinski, Elke, 2004. "Kontroversen in der internationalen Währungspolitik: Retrospektive zu Keynes-White-Boughton & IMF," Discussion Papers 2004/1, Free University Berlin, School of Business & Economics.
    2. Jarque, Carlos M. & Bera, Anil K., 1980. "Efficient tests for normality, homoscedasticity and serial independence of regression residuals," Economics Letters, Elsevier, vol. 6(3), pages 255-259.
    3. Urzua, Carlos M., 1996. "On the correct use of omnibus tests for normality," Economics Letters, Elsevier, vol. 53(3), pages 247-251, December.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    goodness-of-fit tests; tests of Kolmogorov-Smirnov and Cramervon Mises type; Shapiro-Wilk test; Kuiper test; skewness; kurtosis; contaminated normal distribution; Monte-Carlo simulation; critical values; power comparison;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:zbw:fubsbe:20049. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (ZBW - German National Library of Economics). General contact details of provider: http://edirc.repec.org/data/fwfubde.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.