# Jarque-Bera test for Normality

Which test should I consider if by JB-test result I have heteroscedasticity and by the result of two others no.

$JB JB-Test (multivariate)  data: Residuals of VAR object var.2c Chi-squared = 10.051, df = 4, p-value = 0.03958$Skewness

Skewness only (multivariate)


data: Residuals of VAR object var.2c Chi-squared = 5.8453, df = 2, p-value = 0.05379

\$Kurtosis

Kurtosis only (multivariate)


data: Residuals of VAR object var.2c Chi-squared = 4.2056, df = 2, p-value = 0.1221

## 1 Answer

The JB-test (Jarque-Bera test) is a test of normality, not of heteroskedasticity. The JB-test tests whether your sample of data has the same skewness and kurtosis as the normal distribution. You'll recall that the normal distribution has skewness = 0 and kurtosis = 3 (or excess kurtosis = 0). In the first test, you tested for both simultaneously, whereas in the second and third tests you tested for these separately. However, all three tests are test of normality, not heteroskedasticity. See the Breusch-Pagan test for a test of heteroskedasticity.

• You are right....sorry.What about normality in the first test?By a p-value<0.05 I should conclude that the residuals don't have normal distribution?@ColorStatics – Eni Dec 27 '18 at 16:43
• Your null hypothesis is that the data is normally distributed. The result of the first JB test, which uses both skewness and kurtosis, indicates that assuming that the null hypothesis is true (i.e. data is normally distributed), there is a less than 5% chance that you'll observe a sample as extreme (with regards to skewness and kurtosis) as the one you have. Therefore, you reject the null and conclude that the data is not normally distributed. The second and third tests give you the additional insights that the departure from normality is bigger in terms of skewness than in terms of kurtosis. – ColorStatistics Dec 27 '18 at 17:01
• Plot the data to get a better idea of what is going on. You should be able to confirm the above findings visually. – ColorStatistics Dec 27 '18 at 17:03
• Thank you very much.What should I do for having normal distribution?I mean , in this case the estimation of the model is not ok? – Eni Dec 27 '18 at 17:05
• You're welcome. It is difficult to say without knowing more details about your model. I suggest you edit the posting by adding some details about what you are trying to do and what sort of data you are working with. – ColorStatistics Dec 27 '18 at 17:19