For small samples the chi-squared approximation is overly sensitive, often rejecting the null hypothesis when it is true.
The table below shows some p-values approximated by a chi-squared distribution that differ from their true alpha levels for small samples.
(These values have been approximated using Monte Carlo simulation in Matlab) In MATLAB's implementation, the chi-squared approximation for the JB statistic's distribution is only used for large sample sizes (> 2000).
For smaller samples, it uses a table derived from Monte Carlo simulations in order to interpolate p-values.
[1] The statistic was derived by Carlos M. Jarque and Anil K. Bera while working on their Ph.D. Thesis at the Australian National University.
According to Robert Hall, David Lilien, et al. (1995) when using this test along with multiple regression analysis the right estimate is: where n is the number of observations and k is the number of regressors when examining residuals to an equation.