Three Different Measures of Sample Skewness and Kurtosis and their Effects on the Jarque-Bera Test for Normality

Monte Carlo methods are used to study the size and the power of three versions of the Jarque and Bera LM test for normality, JB( 1 2 g , g ), JB( 1 2 b ,b ), and finally JB( 1 2 k ,k ). 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 over-sized for small nominal level and under-sized for larger than 3% levels even in a reasonably large sample. However the JB( 1 2 k ,k ) for a 5% nominal level shows good properties for all samples. The power of the tests shows the same erratic form.