Jarque-Bera Statistics

The Jarque-Bera statistics is used to check the hypothesis that the remainder of examined series is from a normal distribution.

where:

N. Number of observations.
Skewness coefficient:
Kurtosis coefficient:
Variance:
s. Standard deviation based on sample.

Test statistics has χ2 distribution with two degrees of freedom. Null hypothesis of normal distribution of series residuals is rejected at selected significance level, if the Jarque-Bera statistics is greater than critical value of χ2 statistics (critical value of χ2 for significance level 0.01 is 9.2103, for significance level 0.05 it is 5.9916).