Title: Three different measures of sample skewness and kurtosis and their effects on the Jarque–Bera test for normality

Authors: Panagiotis Mantalos

Addresses: Department of Economics and Statistics, Jonkoping International Business School, Jonkoping SE-551 11, Sweden

Abstract: Monte Carlo methods are used to study the size and the power of three versions of the Jarque and Bera Lagrangian multiplier test for normality, JB(g₁, g₂), JB(b₁, b₂) and, finally, JB(k₁, k₂). The difference between these tests comes from the different definitions (estimates) of sample skewness and kurtosis. The Jarque and Bera test has rather poor small sample properties: the slow convergence of the test statistic to its limiting distribution makes the test oversized for small nominal level and undersized for larger than 3% levels even in a reasonably large sample. However, the JB(k₁, k₂) for a 5% nominal level shows good properties for all samples. The power of the tests shows the same erratic form.

Keywords: Jarque and Bera; Lagrangian multiplier test; kurtosis; sample skewness; test for normality; sampling; Monte Carlo methods.

DOI: 10.1504/IJCEE.2011.040576

International Journal of Computational Economics and Econometrics, 2011 Vol.2 No.1, pp.47 - 62

Published online: 07 Jun 2011 *

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