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

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Michele Di Giacomo

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Sep 6, 2021, 11:16:21 AMSep 6
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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

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Sep 6, 2021, 11:25:14 AMSep 6
to pystatsmodels

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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