Robust Critical Values for the Jarque-bera Test for Normality Author: PANAGIOTIS MANTALOS
Origin: Jonkoping International Business School ,and can be found at: hj.se/?d/18.3bf8114412e804c78638000150/WP2010-8.pdf
At two successive pages it can be found: __mu2(g1)= 6*(n-2)/ [(n+1)*(n+3)] _______________(2.4) __mu2(g2)= 24*(n-2)*(n-3)/[(n+1)^2*(n+3)*(n+5)]___(2.6) JB= n* [(g1)^2/ 6 + (g2)^2/ 24]___________________(2.7) And finally (2.11) JBM= n*[(g1)^2 /mu2(g1) + (g2-mu1(g2))/(mu2(g2))
Specifically the author didn´t get that (2.7) is incompatible with the well-known Jarque-Bera statistics, ordinarily written. _________JB= n*[S^2/ 6 + (K-3)^2/ 24], (a former expression to which JBM intends to be an improvement). In fact (2.4) tends as 6/n and (2.8) as 24/n. The n factor at (2.11) has no place to exist, any chance . . . because the variance of S (skewness) and k (excess kurtosis) do tend asymptotically for 6/n and 24/n respectively, and not for 6 and 24 as he thinks. The correction is stated here no matter to be easily detectable.