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Topic: Jarque-Bera Test : A failed objective . . .
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Luis A. Afonso

Posts: 4,758
From: LIsbon (Portugal)
Registered: 2/16/05
Jarque-Bera Test : A failed objective . . .
Posted: Jul 29, 2012 5:09 PM
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Jarque-Bera Test : A failed objective . . .

Currently in literature is stated that the Jarque-Bera test (JB) is one to assert data normality. More precisely: if data leads to a test statistics lower (or equal) to the critical value, i.e. falls into the *acceptance interval*, one should conclude that there is not sufficient evidence that normality doesn?t exist.
The statement is based on an illusory basis: because the critical values are evaluated from exact simulated random samples one is lead to assume that we are dealing with an ordinary Significance Test.
However a closer analysis is necessary.
The test is based on the sum of TWO parameters estimators: the Skewness and Excess Kurtosis after standardized (variance=1) and squared. Let be U and V, then the test statistics is JB= U + V. It´s evident that JB not rejected could be found for example with a very low U and an unlikely large V, so, providing from no normal data. In short: *accepted* test means only that at least one parameter is from likely normal data: to extend to both Skewness and Excess Kurtosis is hazardous.
In conclusion Jarque-Bera Test is not a normality test, even tough there is someone that had remarkably improved the parameters estimators. The error it is NOT at this point, of course.

Luis A. Afonso

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