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Topic: Jarque-Bera: a disastrous test
Replies: 3   Last Post: Feb 26, 2013 7:39 AM

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Luis A. Afonso

Posts: 4,758
From: LIsbon (Portugal)
Registered: 2/16/05
Re: Jarque-Bera: a disastrous test
Posted: Feb 26, 2013 7:39 AM
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In fact suppose , to be clear, that I had the chance to get a value of the test exactly equal to the critical value JBcrit, so, with h=0 :
_____________(U + h) + (V - h) = JBcrit
So, I do not reject.
I will attaint the same decision, not rejection, whatever h.
Now an advise must be pointed out: we are testing a sample issue from an unknown Population W, so all can happens concerning U and V. Suppose, foe example, that S is such that m3=0 approximately (hyper symmetric); in consequence U=0 (whatever the expression providing its standard deviation) and is enough h<= V - JBcrit to not reject normality: Tipe II error. I found people-WEB claiming that the JB test is fertile to commit such kind of errors but I hadn´t notice they get the primary reason that is we are adding two estimates. AND what can I say about the crowd of researchers that try to mend a so failure of test thinking that the concern should be the Skewness and Excess Kurtosis functions and their sample standard deviations and means? Hard to believe, by the other hand, that it was thought that the simple reason normal data could be obtained rigorously by simulation in order to calculate critical values, was sufficient to warrant the test soundness.
Luis A. Afonso

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