Normality of the residuals, Jarque-Bera test, meaning of Chi^2 test for notrmality

[Michele Di Giacomo]

Hi All 
Can anybody
please,
tell me
how to interpret the 'Chi^2 two-tail prob.'
that is provided in output from the
- statsmodels.stats.api  -   jarque_bera(model.resid)

Thanks a lot
mike

[josef...@gmail.com]

https://en.wikipedia.org/wiki/Jarque%E2%80%93Bera_test

https://www.statsmodels.org/dev/generated/statsmodels.stats.stattools.jarque_bera.html

The pvalue has the usual interpretations.

If the pvalue is below a threshold like 0.05, then we reject the null hypothesis.

In this case a small pvalue indicates that the data is not consistent with a normal distribution.

Specifically, Jarque-Bera is a test for skew and kurtosis. 

If the tests rejects, then either skewness or kurtosis or both differe from a normal distribution.

chi2 test are based on a squared test statistic, so the test is always for deviation in the direction of smaller and larger deviations from the null hypothesis.

(always 2-sided for the underlying deviations.)

Josef

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