Jarque-Bera test (JB)

Tests whether a distribution of a random variable follows the normal distribution. Thus, whether its third and fourth moments, the skewness and kurtosis, are equal to the values of a normal distribution: skewness = 0, kurtosis = 3.

Using the error term ( $\hat{u}$ ) of an OLS regression one can estimate these two parameters:

Skewness: $b1 = \frac{E[u^3]}{(\sigma^2)^{3/2}}$

Kurtosis: $b2 = \frac{E[u^4]}{(\sigma^2)^{2}}$

Test statistics:

$W = T[\frac{b_1^2}{6} + \frac{(b_2 - 3)^2}{24}]$

where T is the sample size.

This test statistics follows a Chi² distribution with two degrees of freedom Χ²(2).